Considere a equação:

Sabendo que uma das raízes é o dobro da outra, marque a alternativa que apresenta o produto do numerador pelo denominador de m.

Observe a equação real abaixo:

Sobre a equação supracitada, pode-se afirmar que: 

Durante a prova para um concurso, um candidato deparou-se com a seguinte proposição composta:

Com base em seus conhecimentos de Noções de Lógica, pode-se afirmar que:

A Seção de Educação Física da ESA elaborou uma pesquisa entre 60 alunos do Curso de Formação e Graduação de Sargentos sobre a preferência entre 3 modalidades esportivas: basquete (B), futebol (F) e vôlei (V). Os dados obtidos foram tabelados como se seguem:





Escolhendo-se aleatoriamente um aluno entre os 60 alunos pesquisados, qual a probabilidade de ele preferir, no máximo, uma modalidade esportiva?

O quadrado externo tem lados de medida 5 u.c. e o segmento indicado mede x. Marque a alternativa que apresenta o valor mínimo do lado do quadrado que está inscrito.

Um Pelotão de Infantaria está no terreno representado pelo sistema de coordenadas retangulares abaixo. Sua localização é o ponto P. Em que distância o Pelotão se encontra da Avenida “A”?

A Revolução Pernambucana foi a única rebelião de caráter emancipacionista e republicano, durante o governo de D. João, que ultrapassou a fase da mera conspiração. Marque a alternativa que possui apenas causas da eclosão da Revolução Pernambucana:

I. O apoio incondicional dos Pernambucanos ao governo do Príncipe D. João.
II. A fome no nordeste provocada pela seca de 1816.
III. A concorrência do algodão produzido pelos Norte-Americanos e do açúcar produzido nas Antilhas, que baixavam os preços desses produtos no mercado internacional.
IV. As ideias Monarquistas inspiradas na Revolução Francesa.
V. O crescente aumento dos impostos, após a chegada da corte portuguesa ao Brasil.

A obra machadiana, representada por seus romances e contos, possui duas fases e o livro “Quincas Borba” se encontra na fase da maturidade de Machado, a qual se estabelece, essencialmente, por possuir um teor problematizador, levantando indagações sobre a existência humana, que acaba por ampliar os limites criativos da própria literatura. Nesse contexto, a partir de discussões de vários críticos literários, é muito limitador estabelecer uma Escola Literária única para o autor em questão, contudo, tendo em vista os fatores históricos e características pontuais como as mencionadas, deve-se depreender que a obra é:

A figura abaixo ilustra a propriedade refletora da hipérbole. Se um raio partir de um ponto A e seguir em direção a F₂, então ele é refletido pela hipérbole, no ponto P, e segue em direção a F₁.



Considere a hipérbole 4x ² − 5y ² = 20 de focos F₁ e F₂, com F₁ à esquerda de F₂. Qual das retas abaixo dá a direção do raio que deve partir do ponto A(1,3) para ser refletido no ramo da direita da hipérbole e caminhar em direção a F₁?

Os determinantes são ferramentas com aplicação em diversas áreas de engenharia. Em engenharia de controle, é comum modelar sistemas de controle por meio de matrizes paramétricas. Os engenheiros podem avaliar o comportamento do sistema pelas raízes do polinômio dado pela igualdade det(A − λI) = 0, em que A é a matriz com os parâmetros do sistema; λ é a variável a ser analisada, chamada de autovalores; e I a matriz identidade com a mesma dimensão de A. Dada a equação abaixo, podemos afirmar que os valores de λ que satisfazem a igualdade são:

A ESA terá que elevar a cumeeira do telhado de sua garagem (ponto “C”) para possibilitar a entrada da nova viatura blindada adquirida pelo Exército Brasileiro. Para isso, deverá elevar a cumeeira do telhado da garagem do ponto “C” para o ponto “B”, de modo que a inclinação α do telhado seja dobrada. Sabe-se que: AD̅̅̅̅ = 5m, CD̅̅̅̅ = 1m e CÂD = α. Em quantos metros, aproximadamente, a cumeeira do telhado deverá ser elevada? 

A figura abaixo mostra o triângulo ABC circunscrito em uma circunferência de centro O e raio 3 cm. Determine o perímetro da região sombreada. Considere: BÂC = 90º, α = 30º e π = 3,14.

Read the sentence:

"The soldiers are marching as if their lives depend on it."

Identify the modal verb in the phrase “as if their lives depend on it”.

Read the text and then choose the correct answer to fill the blanks. Be attentive to the coherence of the text and the prepositions you must use or omit before the phrases. 

SPECIAL TALENTS AT THE NCO ACADEMY 

Sergeant Major Gilson commands respect, standing ______ the door of the NCO Academy print workshop and ready to greet his comrades with a gentle smile. He always works diligently ______ his desk, with piles of paperwork and a strong cup of coffee. However, behind closed doors, behind that disciplined facade, there is a secret: a passion for art. His own masterpieces are hanging ______ the walls of his office, showing his remarkable talent as a painter. 

In his quarters, Sergeant Major Gilson devotes all his spare time to painting. Paintbrushes and palettes lie meticulously arranged ______ a shelf. As people rarely see him out of uniform, he surprises everyone with his remarkable talent. When he is not in the barracks, Sergeant Gilson is pursuing a degree in Fine Arts ______ the local college, indulging his passion. 

Late in the evening, after his long day, Sergeant Gilson finally gets ______ home, exhausted but content. He kicks off his boots, relaxes in his favourite chair, and dreams of the next stroke of his brush that will bring his vivid imagination to life.

Read the text. 

    The sergeant major addressed the battalion with a powerful speech. “Courage and discipline,” he said, “are the hallmarks of a true soldier.” The troops felt a surge of pride as they listened. 

Which part of the text contains a possessive case? 

Avoid repetition in text by replacing the underlined phrases with the right pronouns. 

MARIA EDUARDA’S CHANGE OF CAREERS

Maria Eduarda was an English teacher at a private school in Três Corações. Seven years ago, she saw a military parade on Independence Day and thought about joining the Brazilian Army. At first Maria Eduarda’s husband didn’t support Maria Eduarda’s radical career change because Maria Eduarda’s husband was very worried about her radical career change. On the other hand, Maria Eduarda’s mother and father encouraged Maria Eduarda because Maria Eduarda’s mother and father were very proud of their daughter’s decision. Then Maria Eduarda applied for the Army exam and passed it. Now she is a brilliant English Teacher in the Language Teaching Section of the NCO Academy. 

If necessary, fill in the blanks with definite or indefinite articles to have a coherent text. 

BRAZILIAN ARMY REPLACES FN FAL WITH IMBEL IA2 

The IMBEL IA2 rifle is ____ versatile firearm in service in ____ Brazilian Army. The stateowned company IMBEL (Indústria de Material Bélico do Brasil) manufactures the IA2 rifle. It has gradually replaced the outdated FN FAL rifle. 

This modern assault rifle has gained ____ popularity among soldiers due to its exceptional accuracy, durability, and adaptability. The IA2 also offers quick barrel change for different mission requirements. Furthermore, the IA2 possesses tactical rails that enable the attachment of ____ additional accessories such as optics, lasers, and flashlights.

With its exceptional performance and adaptability, the IMBEL IA2 rifle has greatly improved the operational capabilities of the Brazilian Army, making it ____ useful weapon in the defence of ____ Brazil. 

Choose the suitable adjectives to make the text coherent.   

THE ROUTINE OF A MODEL PLATOON SERGEANT 

    The routine of a model platoon sergeant, a crucial figure in a military unit, is ____ of diverse responsibilities and challenges. While they may be ____ at maintaining discipline, they are never ____ with their subordinates. In fact, they understand the importance of being ____ to privates and corporals within the unit.

    Platoon Sergeants are committed to the growth and well-being of their team. They are ____ in their soldiers' professional development, offering guidance and mentorship. They are also devoted to the mission of the unit.

    Like anyone else, platoon sergeants sometimes feel ____ with the demands of their role. However, their commitment remains firm, as they are aware that their actions can influence the success or failure of a mission. If any mistakes occur, they are ____ about the consequences and take responsibility for leading their team to learn and improve.

    The role of a platoon sergeant is ____ from other ranks, requiring strong leadership. While they have moments of fear or hesitation, they do not let it overcome them. They perform their duties with diligence, always aware of the impact on their unit's morale and performance.

Complete the story with the correct indefinite adjectives and pronouns. 

During a patrol a United Nations Peacekeeping mission patrol, Sergeant Reis and his squad scans the surroundings of the area carefully. 

Sergeant Reis: - Everything seems to be calm around here. I see ____ signs of danger but remain on alert. Corporal Santos: - We are vigilant, sir, but I sincerely hope ____ bad happens tonight. However, we are ready to respond to ____ situation.

Private Costa: - There is ____ moving ahead in the darkness,

Sergeant Reis. Can you see it? Is it a dog? Corporal Santos: - I think it’s a person. ____ is coming towards us. 

Sergeant Reis: - Take cover and cock your weapons. I will warn him or her of our presence. We have to follow the rules of engagement. Sergeant Reis: Is ____ there? United Nations! Stop or I’ll shoot! 

     Although the mission is to maintain peace and security, Sergeant Reis is ready to protect his men at any cost and make sure that ____ poses a threat to his unit. 

Use the correct verb tenses to complete the text. 

A BRAZILIAN NCO IN A UN FORCE 

    Sergeant Torres is a Brazilian Platoon Sergeant in a United Nations protection force at a refugee camp in the middle of a war zone. The mission of this force is to protect the refugees from local bandits, militia and the belligerents. A humanitarian organization ____ the camp, while Torres and his comrades provide security. A week ago, fighting ____ the supply route. Despite rationing, Torres and his fellow soldiers ____ nothing to eat for three days and are on their last bottles of water in a hot, dry, desert climate. Refugees, especially children, ____ at an increasing rate now, and the humanitarian worker warns that hundreds more ____ soon if the refugee camp does not receive water and food. Sergeant Torres and the other soldiers remain firm and alert in spite of the signs of dehydration and weakness from starvation.