Magna Concursos

Foram encontradas 70 questões.

2575350 Ano: 2021
Disciplina: Matemática
Banca: ITA
Orgão: ITA
Provas:

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

 

Provas

Questão presente nas seguintes provas
2575349 Ano: 2021
Disciplina: Matemática
Banca: ITA
Orgão: ITA
Provas:

Seja !$ b \in \mathbb{R} !$ tal que a equação

!$ x^2 - 6bx - (1 - b^2)(y^2 - 2by) + b^4 + 8b^2 - 1 = 0 !$

determina uma hipérbole. Com respeito ao centro !$ C !$ desta hipérbole podemos afirmar:

 

Provas

Questão presente nas seguintes provas
2575347 Ano: 2021
Disciplina: Matemática
Banca: ITA
Orgão: ITA
Provas:

Seja !$ n \ge 2 !$ e !$ A, B \in M_n(\mathbb{R}) !$. Considere as seguintes afirmações:

I. Se !$ AB \ne BA !$ então ou !$ A !$ ou !$ B !$ não é inversível.

II. Se !$ AB = 0 !$ então !$ BA = 0 !$.

III. Se !$ A^T = -A^2 !$ e !$ A !$ é inversível então !$ det(A) = -1 !$.

É (são) verdadeira(s):

 

Provas

Questão presente nas seguintes provas
2575346 Ano: 2021
Disciplina: Matemática
Banca: ITA
Orgão: ITA
Provas:

Considere o polinômio !$ p(z) = z^4 - 6z^3 + 14z^2 - 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

 

Provas

Questão presente nas seguintes provas
2575345 Ano: 2021
Disciplina: Matemática
Banca: ITA
Orgão: ITA
Provas:

Sejam !$ z_1, z_2 \in \mathbb{C} !$ com !$ z_2 \ne 0 !$. Considere as afirmações:

I. Se !$ z_1 + z_2 \in \mathbb{R} !$ e !$ z_1 - z_2 \in \mathbb{R} !$ então !$ z_1 \in \mathbb{R} !$ e !$ z_2 \in \mathbb{R} !$.

II. Se !$ z_1 \cdot z_2 \in \mathbb{R} !$ e !$ z_1 / z_2 \in \mathbb{R} !$ então !$ z_1 \in \mathbb{R} !$ e !$ z_2 \in \mathbb{R} !$.

III. Se !$ z_1 + z_2 \in \mathbb{R} !$ e !$ z_1 \cdot z_2 \in \mathbb{R} !$ então !$ z_1 \in \mathbb{R} !$ e !$ z_2 \in \mathbb{R} !$.

É (são) sempre verdadeira(s):

 

Provas

Questão presente nas seguintes provas
2575344 Ano: 2021
Disciplina: Matemática
Banca: ITA
Orgão: ITA
Provas:

Sejam !$ m \in \mathbb{R} !$. Considere os sistemas lineares

!$ S_1: \begin{cases} 4x - y = 2 \\ -16x + m^2y + z = -10 \\ 12x - 3y + z = 8 \end{cases} !$ e !$ S_2: \begin{cases} 10x + z = m^2 + m -1 \\ -5y + 5z = 14 \\ 5my + (14 - 5m)z = 14m^2 -56\end{cases} !$

Assinale a alternativa correta:

 

Provas

Questão presente nas seguintes provas
2575343 Ano: 2021
Disciplina: Matemática
Banca: ITA
Orgão: ITA
Provas:

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 !$. Sabendo que !$ m(\overline{AO}) = 85 !$, !$ m(\overline{AB}) = 10 !$ e !$ m(\overline{BC}) = 24 !$ temos que a distância de !$ O !$ a !$ r !$ é

 

Provas

Questão presente nas seguintes provas
2575342 Ano: 2021
Disciplina: Matemática
Banca: ITA
Orgão: ITA
Provas:

Se

!$ x = 9\log_{120}2 + 3\log_{120}3 + 2\log_{14400}125 !$

podemos afirmar que

 

Provas

Questão presente nas seguintes provas
2575341 Ano: 2021
Disciplina: Inglês (Língua Inglesa)
Banca: ITA
Orgão: ITA
Provas:

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

 

Provas

Questão presente nas seguintes provas
2575340 Ano: 2021
Disciplina: Inglês (Língua Inglesa)
Banca: ITA
Orgão: ITA
Provas:

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

 

Provas

Questão presente nas seguintes provas