Considere as retas !$ r_1 !$ e !$ r_2, !$ no plano, definidas por

!$ \begin {cases} a_1 \, \chi \, + \, b_1 \, y \, + \, c_1 \, = \, 0 \\ a_2 \, \chi \, + \, b_2 \, y \, + \, c_2 \, = \, 0 \end {cases} !$

em que !$ n_1 \, = \, (a_1, \, b_1) !$ e !$ (a_2, \, b_2) !$ são vetores não nulos ortogonais à !$ r_1 !$ e !$ r_2 !$, respectivamente. Denotamos por !$ d(P, \, r) !$ a distância de um ponto !$ P !$ à uma reta !$ r !$ do plano.

Julgue a alternativa:

Item 1 - Se !$ (1,1) \, \in \, r_1 !$ e !$ r_1 !$ é paralela à reta dada por !$ 2\chi \, + \, 3y \, - \, 6 \, = \, 0 !$, então !$ (3,2) \, \in \, r_1. !$

Sobre a Teoria da Produção analise a alternativa abaixo:

Item 4 - A função lucro atende às propriedades de ser homogênea do grau 1 em preços e convexa nos preços.

Considere a função !$ f \, : \, \mathbf{R} \, \rightarrow \, \mathbf{R} !$, definida por !$ f(\chi) \, = \, (\chi \, - \, 2)^2( \chi \, - \, 5) !$, e !$ g \, : \, \mathbf{R} \, \rightarrow \, \mathbf{R} !$, uma função que satisfaz !$ g(\chi \, + \, u) \, = \, g(\chi) \, + \, g(u) \, + \, \chi^2u \, + \, \chi u^2 !$, para todo !$ \chi, \, u \, \in \, \mathbf{R} !$. Julgue a alternativa:

Item 2 - 2 é ponto de máximo relativo de !$ f !$, pois !$ f'(2) \, = \, 0 !$ e !$ f"(2) \, < \, 0. !$

A crise dos anos 1980 foi marcada pelas seguintes circunstâncias:

Item 4 - A indexação generalizada da economia se tornou um mecanismo poderoso de propagação da inflação e também de rigidez dos preços à baixa.

Considere o modelo de regressão linear múltipla

!$ y_t \, = \, \beta_1 \, x_{1t} \, +\, \beta_2 \, x_{2t} \, + \, \varepsilon_t !$

no qual

!$ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, i.i.d \\ \varepsilon_t \, \mid \, X_{1t'}, \, x_{2t'} \sim \, N(0, \, \sigma^2), \, \forall \, t, \, t' \, = \, 1,...,T !$

Por simplicidade, assuma que as variáveis são expressas como desvios em relação às respectivas médias.

É correto afirmar que:

Item 4 - A hipótese de que o erro !$ \varepsilon_t !$ tem média 0 pode ser testada utilizando a estatística !$ (1/T) \, \sum_{i=1}^{T} \hat{ \varepsilon}_t, !$ onde !$ \hat{ \varepsilon}_t !$ é o resíduo da regressão por mínimos quadrados ordinários.

Seja !$ A \, = \, (a_{ij}) !$ uma matriz real !$ n \, \times \, n !$. Considere o sistema !$ A\chi \, = \, b !$ abaixo e julgue a alternativa:

!$ \begin {cases} a_{11} \chi_1 \, + \, a_{12} \chi_{2} \, + \, ... \, + \, a_{1n} \chi_{n} \, = \, b_1 \\ a_{21} \chi_1 \, + \, a_{22} \chi_2 \, + \, ... \, + \, a_{2n} \chi_{n} \, = \, b_2 \\ \,\,\,\,\,\,\,\,\,\, . \\ \,\,\,\,\,\,\,\,\,\, . \\ \,\,\,\,\,\,\,\,\,\, . \\ a_{n1} \chi_{1} \, + \, a_{n2} \chi_2 \, + \, ... \, + \, a_{nn} \chi_n \, = \, b_n \end {cases} !$

Item 1 - Se o vetor b é combinação linear das colunas de A, então o sistema admite solução.

Quanto às políticas cambiais adotadas no Brasil na década posterior à II Guerra Mundial, pode-se afirmar:

Item 2 - O sistema de licenciamento das importações, de acordo com prioridades estabelecidas pelo governo, foi adotado por Dutra e revogado em 1951 com o retorno de Vargas ao poder.

Sobre os planos de combate a inflação das décadas de 1980 e 1990, é correto afirmar:

Item 3 - A execução do Plano Bresser, quando da adoção do congelamento, foi facilitada pela existência de simetria entre os preços relativos.

Text 1

Excerpts from:

The “CSI effect”

Television dramas that rely on forensic science to solve crimes are affecting the administration of justice

Apr 22nd 2010 | From The Economist print edition

OPENING a new training centre in forensic science (...) at the University of Glamorgan in South Wales recently, Bernard Knight, formerly one of Britain’s chief pathologists, said that because of television crime dramas, jurors today expect more categorical proof than forensic science is capable of delivering. And when it comes to the gulf between reality and fiction, Dr Knight knows what he is talking about: besides 43 years’ experience of attending crime scenes, he has also written dozens of crime novels.

The upshot of this is that a new phrase has entered the criminological lexicon: the “CSI effect” after shows such as “CSI: Crime Scene Investigation”. In 2008 Monica Robbers, an American criminologist, defined it as “the phenomenon in which jurors hold unrealistic expectations of forensic evidence and investigation techniques, and have an increased interest in the discipline of forensic science.”

Now another American researcher has demonstrated that the “CSI effect” is indeed real. Evan Durnal of the University of Central Missouri’s Criminal Justice Department has collected evidence from a number of studies to show that exposure to television drama series that focus on forensic science has altered the American legal system in complex and far-reaching ways. His conclusions have just been published in Forensic Science International.

The most obvious symptom of the CSI effect is that jurors think they have a thorough understanding of science they have seen presented on television, when they do not. Mr Durnal cites one case of jurors in a murder trial who, having noticed that a bloody coat introduced as evidence had not been tested for DNA, brought this fact to the judge’s attention. Since the defendant had admitted being present at the murder scene, such tests would have thrown no light on the identity of the true culprit. The judge observed that, thanks to television, jurors knew what DNA tests could do, but not when it was appropriate to use them.

(...)

Criminals watch television too, and there is evidence they are also changing their behaviour. Most of the techniques used in crime shows are, after all, at least grounded in truth. Bleach, which destroys DNA, is now more likely to be used by murderers to cover their tracks. The wearing of gloves is more common, as is the taping shut—rather than the DNA-laden licking—of envelopes. Investigators comb crime scenes ever more finely for new kinds of evidence, which is creating problems with the tracking and storage of evidence, so that even as the criminals leave fewer traces of themselves behind, a backlog of cold-case evidence is building up.

The CSI effect can also be positive, however. In one case in Virginia jurors asked the judge if a cigarette butt had been tested for possible DNA matches to the defendant in a murder trial. It had, but the defence lawyers had failed to introduce the DNA test results as evidence. When they did, those results exonerated the defendant, who was acquitted.

Mr Durnal does not blame the makers of the television shows for the phenomenon, because they have never claimed their shows are completely accurate. (Forensic scientists do not usually wield guns or arrest people, for one thing, and tests that take minutes on television may take weeks to process in real life.) He argues that the CSI effect is born of a longing to believe that desirable, clever and morally unimpeachable individuals are fighting to clear the names of the innocent and put the bad guys behind bars. In that respect, unfortunately, life does not always imitate art.

According to the text, Bernard Knight:

Item 2 - rejected any influence of TV crime dramas involving forensic science on the administration of justice;