ITA 2017
100 Questões
Sejam X e Y dois conjuntos finitos com X ⊂ Y e X <style type="text/css"><!--td {border: 1px solid #cccccc;}br {mso-data-placement:same-cell;}--> </style> ≠ Y . Considere as seguintes afirmações:
I. Existe uma bijeção f : X → Y .
II. Existe uma função injetora g : Y → X.
III. O número de funções injetoras f : X → Y é igual ao número de funções sobrejetoras g : Y → X.
É (são) verdadeira(s)
Ondas gravitacionais foram previstas por Einstein em 1916 e diretamente detectadas pela primeira vez em 2015. Sob determinadas condições, um sistema girando com velocidade angular w irradia tais ondas com potência proporcional a GcβQγwδ , em que G é a constante de gravitação universal; c, a velocidade da luz e Q, uma grandeza que tem unidade em kg.m2 . Assinale a opção correta.
Pode-se utilizar metais de sacrifício para proteger estruturas de aço (tais como pontes, antenas e cascos de navios) da corrosão eletroquímica. Considere os seguintes metais:
I. Alumínio
II. Magnésio
III. Paládio
IV. Sódio
V. Zinco
Assinale a opção que apresenta o(s) metal(is) de sacrifício que pode(m) ser utilizado(s).
FRAYING AT THE EDGES: A LIFE-CH ANGING DI AGNOSIS
[1] IT BEGAN WITH what she saw in the bathroom mirror. On a dull morning, Geri Taylor padded into
the shiny bathroom of her Manhattan apartment. She casually checked her reflection in the mirror, doing her
daily inventory. Immediately, she stiffened with fright.
Huh? What?
[5] She didn‘t recognize herself.
She gazed saucer-eyed at her image, thinking: Oh, is this what I look like? No, that‘s not me. Who‘s
that in my mirror?
This was in late 2012. She was 69, in her early months getting familiar with retirement. For some time
she had experienced the sensation of clouds coming over her, mantling thought. There had been a few
[10] hiccups at her job. She had been a nurse who climbed the rungs to health care executive. Once, she was
leading a staff meeting when she had no idea what she was talking about, her mind like a stalled engine that
wouldn‘t turn over.
"Fortunately I was the boss and I just said, ‗Enough of that; Sally, tell me what you‘re up to," she would
say of the episode.
[15] Certain mundane tasks stumped her. She told her husband, Jim Taylor, that the blind in the bedroom
was broken. He showed her she was pulling the wrong cord. Kept happening. Finally, nothing else working,
he scribbled on the adjacent wall which cord was which.
Then there was the day she got off the subway at 14th Street and Seventh Avenue unable to figure out
why she was there.
[20] So, yes, she had had inklings that something was going wrong with her mind. She held tight to these
thoughts. She even hid her suspicions from Mr. Taylor, who chalked up her thinning memory to the infirmities
of age.
"I thought she was getting like me," he said. "I had been forgetful for 10 years".
But to not recognize her own face! To Ms. Taylor, this was the "drop-dead moment" when she had to
[25] accept a terrible truth. She wasn‘t just seeing the twitches of aging but the early fumes of the disease.
She had no further issues with mirrors, but there was no ignoring that something important had
happened. She confided her fears to her husband and made an appointment with a neurologist.
"Before then I thought I could fake it,' she would explain. "This convinced me I had to come clean"
In November 2012, she saw the neurologist who was treating her migraines. He listened to her
[30] symptoms, took blood, gave her the Mini Mental State Examination, a standard cognitive test made up of a
set of unremarkable questions and commands. (For instance, she was asked to count backward from 100 in
intervals of seven; she had to say the phrase: "No ifs, ands or buts"; she was told to pick up a piece of paper,
fold it in half and place it on the floor beside her.)
He told her three common words, said he was going to ask her them in a little bit. He emphasized this
[35] by pointing a finger at his head — remember those words. That simple. Yet when he called for them, she
knew only one: Beach. In her mind, she would go on to associate it with the doctor, thinking of him as Dr.
Beach.
He gave a diagnosis of mild cognitive impairment, a common precursor to Alzheimer‘s disease. The
first label put on what she had. Even then, she understood it was the footfall of what would come. Alzheimer‘s
[40] had struck her father, a paternal aunt and a cousin. She long suspected it would eventually find her.
Fonte: http://www.nytimes.com/interactive/2016/05/01/nyregion/living-with-alzheimers.html?action=click&contentCollection=Americas&module= Trending&version=Full®ion= Marginalia&pgtype=article. (acesso em 1/05/2016).
Quanto ao gênero textual, o texto pode ser classificado como
FRAYING AT THE EDGES: A LIFE-CH ANGING DI AGNOSIS
[1] IT BEGAN WITH what she saw in the bathroom mirror. On a dull morning, Geri Taylor padded into
the shiny bathroom of her Manhattan apartment. She casually checked her reflection in the mirror, doing her
daily inventory. Immediately, she stiffened with fright.
Huh? What?
[5] She didn‘t recognize herself.
She gazed saucer-eyed at her image, thinking: Oh, is this what I look like? No, that‘s not me. Who‘s
that in my mirror?
This was in late 2012. She was 69, in her early months getting familiar with retirement. For some time
she had experienced the sensation of clouds coming over her, mantling thought. There had been a few
[10] hiccups at her job. She had been a nurse who climbed the rungs to health care executive. Once, she was
leading a staff meeting when she had no idea what she was talking about, her mind like a stalled engine that
wouldn‘t turn over.
"Fortunately I was the boss and I just said, ‗Enough of that; Sally, tell me what you‘re up to," she would
say of the episode.
[15] Certain mundane tasks stumped her. She told her husband, Jim Taylor, that the blind in the bedroom
was broken. He showed her she was pulling the wrong cord. Kept happening. Finally, nothing else working,
he scribbled on the adjacent wall which cord was which.
Then there was the day she got off the subway at 14th Street and Seventh Avenue unable to figure out
why she was there.
[20] So, yes, she had had inklings that something was going wrong with her mind. She held tight to these
thoughts. She even hid her suspicions from Mr. Taylor, who chalked up her thinning memory to the infirmities
of age.
"I thought she was getting like me," he said. "I had been forgetful for 10 years".
But to not recognize her own face! To Ms. Taylor, this was the "drop-dead moment" when she had to
[25] accept a terrible truth. She wasn‘t just seeing the twitches of aging but the early fumes of the disease.
She had no further issues with mirrors, but there was no ignoring that something important had
happened. She confided her fears to her husband and made an appointment with a neurologist.
"Before then I thought I could fake it,' she would explain. "This convinced me I had to come clean"
In November 2012, she saw the neurologist who was treating her migraines. He listened to her
[30] symptoms, took blood, gave her the Mini Mental State Examination, a standard cognitive test made up of a
set of unremarkable questions and commands. (For instance, she was asked to count backward from 100 in
intervals of seven; she had to say the phrase: "No ifs, ands or buts"; she was told to pick up a piece of paper,
fold it in half and place it on the floor beside her.)
He told her three common words, said he was going to ask her them in a little bit. He emphasized this
[35] by pointing a finger at his head — remember those words. That simple. Yet when he called for them, she
knew only one: Beach. In her mind, she would go on to associate it with the doctor, thinking of him as Dr.
Beach.
He gave a diagnosis of mild cognitive impairment, a common precursor to Alzheimer‘s disease. The
first label put on what she had. Even then, she understood it was the footfall of what would come. Alzheimer‘s
[40] had struck her father, a paternal aunt and a cousin. She long suspected it would eventually find her.
Fonte: http://www.nytimes.com/interactive/2016/05/01/nyregion/living-with-alzheimers.html?action=click&contentCollection=Americas&module= Trending&version=Full®ion= Marginalia&pgtype=article. (acesso em 1/05/2016).
Quanto à narrativa, o texto é apresentado
O número de soluções da equação (1 + secθ)(1 + cossecθ) = 0, com θ ∈ [−π, π], é