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Q1901481 Matemática
Convenções: Consideramos o sistema de coordenadas cartesiano a menos que haja indicação contrária.
N = {1, 2, 3, . . . } : denota o conjunto dos números naturais.
R : denota o conjunto dos números reais.
C : denota o conjunto dos números complexos.
i : denota a unidade imaginária, i2 = −1.
Mn(R) : denota o conjunto das matrizes n × n de entradas reais.
: denota o segmento de reta de extremidades nos pontos A e B.
 : denota o ângulo formado pelas semi-retas  e , com vértice no ponto O.
 : denota o comprimento do segmento .
O número de soluções reais e distintas da equação
cos2 (2x) = 3 − cos6 (x) − 5 cos2 (x)
no intervalo [0, 2π[ é
Alternativas
Q1901480 Matemática
Convenções: Consideramos o sistema de coordenadas cartesiano a menos que haja indicação contrária.
N = {1, 2, 3, . . . } : denota o conjunto dos números naturais.
R : denota o conjunto dos números reais.
C : denota o conjunto dos números complexos.
i : denota a unidade imaginária, i2 = −1.
Mn(R) : denota o conjunto das matrizes n × n de entradas reais.
: denota o segmento de reta de extremidades nos pontos A e B.
 : denota o ângulo formado pelas semi-retas  e , com vértice no ponto O.
 : denota o comprimento do segmento .
Sejam α, β e θ ângulos internos de um triângulo. Se cos(β + θ) ≤ cos(α + 2β), podemos afirmar que: 
Alternativas
Q1901479 Matemática
Convenções: Consideramos o sistema de coordenadas cartesiano a menos que haja indicação contrária.
N = {1, 2, 3, . . . } : denota o conjunto dos números naturais.
R : denota o conjunto dos números reais.
C : denota o conjunto dos números complexos.
i : denota a unidade imaginária, i2 = −1.
Mn(R) : denota o conjunto das matrizes n × n de entradas reais.
: denota o segmento de reta de extremidades nos pontos A e B.
 : denota o ângulo formado pelas semi-retas  e , com vértice no ponto O.
 : denota o comprimento do segmento .
Seja A o conjunto de todas as retas que passam por dois vértices distintos de um cubo C. Escolhendo aleatoriamente duas retas distintas de A, a probabilidade dessas retas se interceptarem em um vértice de C é:
Alternativas
Q1901478 Matemática
Convenções: Consideramos o sistema de coordenadas cartesiano a menos que haja indicação contrária.
N = {1, 2, 3, . . . } : denota o conjunto dos números naturais.
R : denota o conjunto dos números reais.
C : denota o conjunto dos números complexos.
i : denota a unidade imaginária, i2 = −1.
Mn(R) : denota o conjunto das matrizes n × n de entradas reais.
: denota o segmento de reta de extremidades nos pontos A e B.
 : denota o ângulo formado pelas semi-retas  e , com vértice no ponto O.
 : denota o comprimento do segmento .
Dizemos que a representação binária de um número NN da forma
N = g · 20 + f · 21 + e · 22 + d · 23 + c · 24 + b · 25 + a · 26
é (abcdefg)2, onde a, b, c, d, e, f, g ∈ {0, 1} e omitem-se os algarismos 0 até o primeiro algarismo 1 da esquerda para a direita. Seja k um número inteiro tal que 1 ≤ k ≤ 100. Qual a probabilidade de k e k + 1 terem representações binárias com um número distinto de algarismos? 
Alternativas
Q1901477 Raciocínio Lógico
Convenções: Consideramos o sistema de coordenadas cartesiano a menos que haja indicação contrária.
N = {1, 2, 3, . . . } : denota o conjunto dos números naturais.
R : denota o conjunto dos números reais.
C : denota o conjunto dos números complexos.
i : denota a unidade imaginária, i2 = −1.
Mn(R) : denota o conjunto das matrizes n × n de entradas reais.
: denota o segmento de reta de extremidades nos pontos A e B.
 : denota o ângulo formado pelas semi-retas  e , com vértice no ponto O.
 : denota o comprimento do segmento .
Considere as seguintes afirmações:
I. Se α e β são planos paralelos distintos e r é uma reta tal que rα 6= ∅ então r β 6= ∅.
II. Se r é uma reta e P e Q são pontos distintos, então existem infinitos planos equidistantes de P e Q que contêm r.
III. Dado quatro pontos no espaço, existe um único ponto equidistante a eles.
É (são) verdadeira(s):
Alternativas
Q1901476 Matemática
Convenções: Consideramos o sistema de coordenadas cartesiano a menos que haja indicação contrária.
N = {1, 2, 3, . . . } : denota o conjunto dos números naturais.
R : denota o conjunto dos números reais.
C : denota o conjunto dos números complexos.
i : denota a unidade imaginária, i2 = −1.
Mn(R) : denota o conjunto das matrizes n × n de entradas reais.
: denota o segmento de reta de extremidades nos pontos A e B.
 : denota o ângulo formado pelas semi-retas  e , com vértice no ponto O.
 : denota o comprimento do segmento .
Seja P uma pirâmide regular cujo vértice V é um dos vértices de um cubo de lado l e cuja base é o hexágono formado pelos pontos médios das seis arestas do cubo que não contém V nem o vértice oposto a V. O raio da esfera que circunscreve P é
Alternativas
Q1901475 Matemática
Convenções: Consideramos o sistema de coordenadas cartesiano a menos que haja indicação contrária.
N = {1, 2, 3, . . . } : denota o conjunto dos números naturais.
R : denota o conjunto dos números reais.
C : denota o conjunto dos números complexos.
i : denota a unidade imaginária, i2 = −1.
Mn(R) : denota o conjunto das matrizes n × n de entradas reais.
: denota o segmento de reta de extremidades nos pontos A e B.
 : denota o ângulo formado pelas semi-retas  e , com vértice no ponto O.
 : denota o comprimento do segmento .
Seja b ∈ R tal que a equação
x2 − 6bx − (1 − b2)(y2 − 2by) + b4 + 8b2 − 1 = 0
determina uma hipérbole. Com respeito ao centro C desta hipérbole podemos afirmar: 
Alternativas
Q1901474 Matemática
Convenções: Consideramos o sistema de coordenadas cartesiano a menos que haja indicação contrária.
N = {1, 2, 3, . . . } : denota o conjunto dos números naturais.
R : denota o conjunto dos números reais.
C : denota o conjunto dos números complexos.
i : denota a unidade imaginária, i2 = −1.
Mn(R) : denota o conjunto das matrizes n × n de entradas reais.
: denota o segmento de reta de extremidades nos pontos A e B.
 : denota o ângulo formado pelas semi-retas  e , com vértice no ponto O.
 : denota o comprimento do segmento .
Sejam x, r ∈ R e suponha que
−π/2 < xr x + r < π/2.
Sobre
tan(x − r),tan(x) e tan(x + r),
nesta ordem, podemos afirmar que:
Alternativas
Q1901473 Matemática
Convenções: Consideramos o sistema de coordenadas cartesiano a menos que haja indicação contrária.
N = {1, 2, 3, . . . } : denota o conjunto dos números naturais.
R : denota o conjunto dos números reais.
C : denota o conjunto dos números complexos.
i : denota a unidade imaginária, i2 = −1.
Mn(R) : denota o conjunto das matrizes n × n de entradas reais.
: denota o segmento de reta de extremidades nos pontos A e B.
 : denota o ângulo formado pelas semi-retas  e , com vértice no ponto O.
 : denota o comprimento do segmento .
Seja n ≥ 2 e A, BMn(R). Considere as seguintes afirmações:
I. Se AB  BA então ou A ou B não é inversível.
II. Se AB = 0 então BA = 0.
III. Se AT = −A2 e A é inversível então det(A) = −1.
É (são) verdadeira(s):
Alternativas
Q1901472 Matemática
Convenções: Consideramos o sistema de coordenadas cartesiano a menos que haja indicação contrária.
N = {1, 2, 3, . . . } : denota o conjunto dos números naturais.
R : denota o conjunto dos números reais.
C : denota o conjunto dos números complexos.
i : denota a unidade imaginária, i2 = −1.
Mn(R) : denota o conjunto das matrizes n × n de entradas reais.
: denota o segmento de reta de extremidades nos pontos A e B.
 : denota o ângulo formado pelas semi-retas  e , com vértice no ponto O.
 : denota o comprimento do segmento .
Considere o polinômio p(z) = z4−6z3+ 14z2−6z+ 13 e note que p(i) = 0. Considere no plano complexo o quadrilátero cujos vértices são as raízes de p(z). Podemos afirmar a área desse quadrilátero é
Alternativas
Q1901471 Raciocínio Lógico
Convenções: Consideramos o sistema de coordenadas cartesiano a menos que haja indicação contrária.
N = {1, 2, 3, . . . } : denota o conjunto dos números naturais.
R : denota o conjunto dos números reais.
C : denota o conjunto dos números complexos.
i : denota a unidade imaginária, i2 = −1.
Mn(R) : denota o conjunto das matrizes n × n de entradas reais.
: denota o segmento de reta de extremidades nos pontos A e B.
 : denota o ângulo formado pelas semi-retas  e , com vértice no ponto O.
 : denota o comprimento do segmento .
Sejam z1, z2 ∈ C com z 0. Considere as afirmações: 
I. Se z1 + z2 ∈ R e z1z2 ∈ R então z1 ∈ R e z2 ∈ R.
II. Se z1 · z2 ∈ R e z1/z2 ∈ R então z1 ∈ R e z2 ∈ R.
III. Se z1 + z2 ∈ R e z1 · z2 ∈ R então z1 ∈ R e z2 ∈ R.
É (são) sempre verdadeira(s):
Alternativas
Q1901470 Matemática
Convenções: Consideramos o sistema de coordenadas cartesiano a menos que haja indicação contrária.
N = {1, 2, 3, . . . } : denota o conjunto dos números naturais.
R : denota o conjunto dos números reais.
C : denota o conjunto dos números complexos.
i : denota a unidade imaginária, i2 = −1.
Mn(R) : denota o conjunto das matrizes n × n de entradas reais.
: denota o segmento de reta de extremidades nos pontos A e B.
 : denota o ângulo formado pelas semi-retas  e , com vértice no ponto O.
 : denota o comprimento do segmento .
Seja m ∈ R. Considere os sistemas lineares 
Imagem associada para resolução da questão
Assinale a alternativa correta: 
Alternativas
Q1901469 Matemática
Convenções: Consideramos o sistema de coordenadas cartesiano a menos que haja indicação contrária.
N = {1, 2, 3, . . . } : denota o conjunto dos números naturais.
R : denota o conjunto dos números reais.
C : denota o conjunto dos números complexos.
i : denota a unidade imaginária, i2 = −1.
Mn(R) : denota o conjunto das matrizes n × n de entradas reais.
: denota o segmento de reta de extremidades nos pontos A e B.
 : denota o ângulo formado pelas semi-retas  e , com vértice no ponto O.
 : denota o comprimento do segmento .
Considere um triângulo de vértices A, B e C, retângulo em B. Seja r a reta determinada por A e C e seja O um ponto equidistante de A e C no mesmo lado que B com respeito a r. Sabendo que Imagem associada para resolução da questão = 85, Imagem associada para resolução da questão = 10 e Imagem associada para resolução da questão = 24 temos que a distância de O a r é
Alternativas
Q1901468 Matemática
Convenções: Consideramos o sistema de coordenadas cartesiano a menos que haja indicação contrária.
N = {1, 2, 3, . . . } : denota o conjunto dos números naturais.
R : denota o conjunto dos números reais.
C : denota o conjunto dos números complexos.
i : denota a unidade imaginária, i2 = −1.
Mn(R) : denota o conjunto das matrizes n × n de entradas reais.
: denota o segmento de reta de extremidades nos pontos A e B.
 : denota o ângulo formado pelas semi-retas  e , com vértice no ponto O.
 : denota o comprimento do segmento .
Se
x = 9 log120 2 + 3 log120 3 + 2 log14400 125
podemos afirmar que
Alternativas
Q1901467 Inglês
Leia o texto destacado para responder à questão.

Meritocracy has become a leading social ideal. Politicians across the ideological spectrum continually return to the theme that the rewards of life—money, power, jobs, university admission—should be distributed according to skill and effort. The most common metaphor is the ‘even playing field’ upon which players can rise to the position that fits their merit. Conceptually and morally, meritocracy is presented as the opposite of systems such as hereditary aristocracy, in which one’s social position is determined by the lottery of birth. Under meritocracy, wealth and advantage are merit’s rightful compensation, not the fortuitous windfall of external events. And most people don’t just think the world should be run meritocratically, they think it is meritocratic. However, although widely held, the belief that merit rather than luck determines success or failure in the world is demonstrably false. This is not least because merit itself is, in large part, the result of luck. Talent and the capacity for determined effort, sometimes called ‘grit’, depend a great deal on one’s genetic endowments and upbringing.
Perhaps more disturbing, simply holding meritocracy as a value seems to promote discriminatory behaviour. The management scholar Emilio Castilla at the Massachusetts Institute of Technology and the sociologist Stephen Benard at Indiana University studied attempts to implement meritocratic practices, such as performance-based compensation in private companies. They found that, in companies that explicitly held meritocracy as a core value, managers assigned greater rewards to male employees over female employees with identical performance evaluations. This preference disappeared where meritocracy was not explicitly adopted as a value.
This is surprising because impartiality is the core of meritocracy’s moral appeal. The ‘even playing field’ is intended to avoid unfair inequalities based on gender, race and the like. Yet  Castilla and Benard found that, ironically, attempts to implement meritocracy leads to just the kinds of inequalities that it aims to eliminate. They suggest that this ‘paradox of meritocracy’ occurs because explicitly adopting meritocracy as a value convinces subjects of their own moral sincerity. Satisfied that they are just, they become less inclined to examine their own behaviour for signs of prejudice.
As with any ideology, part of its draw is that it justifies the status quo, explaining why people belong where they happen to be in the social order. It is a well-established psychological principle that people prefer to believe that the world is just.

Fonte: https://bigthink.com/. Publicado em 23/03/2019. Acesso em 20/08/2021. Adaptado.
De acordo com o quarto parágrafo, a meritocracia promove 
Alternativas
Q1901466 Inglês
Leia o texto destacado para responder à questão.

Meritocracy has become a leading social ideal. Politicians across the ideological spectrum continually return to the theme that the rewards of life—money, power, jobs, university admission—should be distributed according to skill and effort. The most common metaphor is the ‘even playing field’ upon which players can rise to the position that fits their merit. Conceptually and morally, meritocracy is presented as the opposite of systems such as hereditary aristocracy, in which one’s social position is determined by the lottery of birth. Under meritocracy, wealth and advantage are merit’s rightful compensation, not the fortuitous windfall of external events. And most people don’t just think the world should be run meritocratically, they think it is meritocratic. However, although widely held, the belief that merit rather than luck determines success or failure in the world is demonstrably false. This is not least because merit itself is, in large part, the result of luck. Talent and the capacity for determined effort, sometimes called ‘grit’, depend a great deal on one’s genetic endowments and upbringing.
Perhaps more disturbing, simply holding meritocracy as a value seems to promote discriminatory behaviour. The management scholar Emilio Castilla at the Massachusetts Institute of Technology and the sociologist Stephen Benard at Indiana University studied attempts to implement meritocratic practices, such as performance-based compensation in private companies. They found that, in companies that explicitly held meritocracy as a core value, managers assigned greater rewards to male employees over female employees with identical performance evaluations. This preference disappeared where meritocracy was not explicitly adopted as a value.
This is surprising because impartiality is the core of meritocracy’s moral appeal. The ‘even playing field’ is intended to avoid unfair inequalities based on gender, race and the like. Yet  Castilla and Benard found that, ironically, attempts to implement meritocracy leads to just the kinds of inequalities that it aims to eliminate. They suggest that this ‘paradox of meritocracy’ occurs because explicitly adopting meritocracy as a value convinces subjects of their own moral sincerity. Satisfied that they are just, they become less inclined to examine their own behaviour for signs of prejudice.
As with any ideology, part of its draw is that it justifies the status quo, explaining why people belong where they happen to be in the social order. It is a well-established psychological principle that people prefer to believe that the world is just.

Fonte: https://bigthink.com/. Publicado em 23/03/2019. Acesso em 20/08/2021. Adaptado.
According to the third and fourth paragraphs, researchers at the Massachusetts Institute of Technology and Indiana University found that meritocracy 
Alternativas
Q1901465 Inglês
Leia o texto destacado para responder à questão.

Meritocracy has become a leading social ideal. Politicians across the ideological spectrum continually return to the theme that the rewards of life—money, power, jobs, university admission—should be distributed according to skill and effort. The most common metaphor is the ‘even playing field’ upon which players can rise to the position that fits their merit. Conceptually and morally, meritocracy is presented as the opposite of systems such as hereditary aristocracy, in which one’s social position is determined by the lottery of birth. Under meritocracy, wealth and advantage are merit’s rightful compensation, not the fortuitous windfall of external events. And most people don’t just think the world should be run meritocratically, they think it is meritocratic. However, although widely held, the belief that merit rather than luck determines success or failure in the world is demonstrably false. This is not least because merit itself is, in large part, the result of luck. Talent and the capacity for determined effort, sometimes called ‘grit’, depend a great deal on one’s genetic endowments and upbringing.
Perhaps more disturbing, simply holding meritocracy as a value seems to promote discriminatory behaviour. The management scholar Emilio Castilla at the Massachusetts Institute of Technology and the sociologist Stephen Benard at Indiana University studied attempts to implement meritocratic practices, such as performance-based compensation in private companies. They found that, in companies that explicitly held meritocracy as a core value, managers assigned greater rewards to male employees over female employees with identical performance evaluations. This preference disappeared where meritocracy was not explicitly adopted as a value.
This is surprising because impartiality is the core of meritocracy’s moral appeal. The ‘even playing field’ is intended to avoid unfair inequalities based on gender, race and the like. Yet  Castilla and Benard found that, ironically, attempts to implement meritocracy leads to just the kinds of inequalities that it aims to eliminate. They suggest that this ‘paradox of meritocracy’ occurs because explicitly adopting meritocracy as a value convinces subjects of their own moral sincerity. Satisfied that they are just, they become less inclined to examine their own behaviour for signs of prejudice.
As with any ideology, part of its draw is that it justifies the status quo, explaining why people belong where they happen to be in the social order. It is a well-established psychological principle that people prefer to believe that the world is just.

Fonte: https://bigthink.com/. Publicado em 23/03/2019. Acesso em 20/08/2021. Adaptado.
According to the first paragraph, one of the supporting arguments for meritocracy is:  
Alternativas
Q1901464 Inglês
Leia o texto destacado para responder à questão.

In a new survey of North American Indian languages, Marianne Mithun gives an admirably clear statement of what is lost as each language ceases to be used. “Speakers of these languages and their descendants are acutely aware of what it can mean to lose a language,” she begins – and this is perfectly true, although these speakers must have taken the decision themselves not to teach the language to their children. It happens all too often – people regret that their language and culture are being lost but at the same time decide not to saddle their own children with the chore of preserving them.
When a language disappears [Mithun continues] the most intimate aspects of culture can disappear as well: fundamental ways of organizing experience into concepts, of relating ideas to each other, of interacting to people. The more conscious genres of verbal art are usually lost as well: traditional ritual, oratory, myth, legends, and even humor. Speakers commonly remark that when they speak a different language, they say different things and even think different thoughts. These are very interesting assertions. They slip by in a book on anthropological linguistics, where in a book on linguistic theory they would be highly contentious. Is it true that “fundamental ways of organizing experience into concepts [and] of relating ideas to each other” are specific to individual languages and are therefore likely to be lost when a language ceases to be used? Is it true that when speakers speak a different language, they “say different things and even think different thoughts”? Again, the extent to which thought depends on language is very controversial. These questions must be now faced, because only when we have reached an opinion on them will we be able to accept or reject Marianne Mithun’s conclusion: “The loss of a language represents a definitive separation of a people from its heritage. It also represents an irreparable loss for us all, the loss of opportunities to glimpse alternative ways of making sense of the human experience.”

Fonte: Dalby, Andrew. Language in danger. New York: Columbia University Press, 2003, p. 252; 285. Adaptado.  
De acordo com o texto, é correto afirmar que com o desaparecimento de uma língua, aspectos dessa cultura também estão fadados ao desaparecimento, exceto 
Alternativas
Q1901463 Inglês
Leia o texto destacado para responder à questão.

In a new survey of North American Indian languages, Marianne Mithun gives an admirably clear statement of what is lost as each language ceases to be used. “Speakers of these languages and their descendants are acutely aware of what it can mean to lose a language,” she begins – and this is perfectly true, although these speakers must have taken the decision themselves not to teach the language to their children. It happens all too often – people regret that their language and culture are being lost but at the same time decide not to saddle their own children with the chore of preserving them.
When a language disappears [Mithun continues] the most intimate aspects of culture can disappear as well: fundamental ways of organizing experience into concepts, of relating ideas to each other, of interacting to people. The more conscious genres of verbal art are usually lost as well: traditional ritual, oratory, myth, legends, and even humor. Speakers commonly remark that when they speak a different language, they say different things and even think different thoughts. These are very interesting assertions. They slip by in a book on anthropological linguistics, where in a book on linguistic theory they would be highly contentious. Is it true that “fundamental ways of organizing experience into concepts [and] of relating ideas to each other” are specific to individual languages and are therefore likely to be lost when a language ceases to be used? Is it true that when speakers speak a different language, they “say different things and even think different thoughts”? Again, the extent to which thought depends on language is very controversial. These questions must be now faced, because only when we have reached an opinion on them will we be able to accept or reject Marianne Mithun’s conclusion: “The loss of a language represents a definitive separation of a people from its heritage. It also represents an irreparable loss for us all, the loss of opportunities to glimpse alternative ways of making sense of the human experience.”

Fonte: Dalby, Andrew. Language in danger. New York: Columbia University Press, 2003, p. 252; 285. Adaptado.  
O termo “must”, destacado em itálico no excerto do segundo parágrafo, “These questions must be now faced”, pode ser substituído, sem alteração de significado, por 
Alternativas
Q1901462 Inglês
Leia o texto destacado para responder à questão.

In a new survey of North American Indian languages, Marianne Mithun gives an admirably clear statement of what is lost as each language ceases to be used. “Speakers of these languages and their descendants are acutely aware of what it can mean to lose a language,” she begins – and this is perfectly true, although these speakers must have taken the decision themselves not to teach the language to their children. It happens all too often – people regret that their language and culture are being lost but at the same time decide not to saddle their own children with the chore of preserving them.
When a language disappears [Mithun continues] the most intimate aspects of culture can disappear as well: fundamental ways of organizing experience into concepts, of relating ideas to each other, of interacting to people. The more conscious genres of verbal art are usually lost as well: traditional ritual, oratory, myth, legends, and even humor. Speakers commonly remark that when they speak a different language, they say different things and even think different thoughts. These are very interesting assertions. They slip by in a book on anthropological linguistics, where in a book on linguistic theory they would be highly contentious. Is it true that “fundamental ways of organizing experience into concepts [and] of relating ideas to each other” are specific to individual languages and are therefore likely to be lost when a language ceases to be used? Is it true that when speakers speak a different language, they “say different things and even think different thoughts”? Again, the extent to which thought depends on language is very controversial. These questions must be now faced, because only when we have reached an opinion on them will we be able to accept or reject Marianne Mithun’s conclusion: “The loss of a language represents a definitive separation of a people from its heritage. It also represents an irreparable loss for us all, the loss of opportunities to glimpse alternative ways of making sense of the human experience.”

Fonte: Dalby, Andrew. Language in danger. New York: Columbia University Press, 2003, p. 252; 285. Adaptado.  
De acordo com a linguista Marianne Mithun  
Alternativas
Respostas
8781: C
8782: C
8783: A
8784: C
8785: A
8786: D
8787: C
8788: D
8789: E
8790: D
8791: A
8792: C
8793: E
8794: B
8795: A
8796: E
8797: B
8798: D
8799: C
8800: B