ITA 2018
100 Questões
Os lados de um triângulo de vértices A, B e C medem AB = 3 cm, BC = 7 cm e CA = 8 cm. A circunferência inscrita no triângulo tangencia o lado AB no ponto N e o lado CA no ponto K. Então, o comprimento do segmento NK, em cm, é
Considere uma estrela de neutrons com densidade média de 5 × 1014 g/cm3 , sendo que sua frequência de vibração radial ν é função do seu raio R, de sua massa m e da constante da gravitação universal G. Sabe-se que ν é dada por uma expressão monomial, em que a constante adimensional de proporcionalidade vale aproximadamente 1. Então o valor de ν é da ordem de
Aminoácidos são compostos orgânicos que contêm um grupo amina e um grupo carboxílico. Nos oc- aminoácidos, os dois grupos encontram-se nas extremidades da molécula e entre eles há um átomo de carbono, denominado carbono-oc, que também está ligado a um grupo R, conforme a figura.
Considere os seguintes aminoácidos:
I. Alanina, em que R = CH3.
II. Asparagina, em que R = CH2CONH2.
III. Fenilalanina, em que R = CH2C6H5.
IV. Glicina, em que R = H.
V. Serina, em que R = CH2OH.
Assinale a opção que contém o(s) aminoácido(s) que possui(em) grupo(s) R polar(es).
As questões de 1 a 6 referem-se ao texto a seguir:
GOODBYE THINGS, HELLO MINIMALISM: CAN LIVING WITH LESS MAKE YOU HAPPIER?
Fumio Sasaki owns a roll-up mattress, three shirts and four pairs of socks. After deciding to scorn possessions, he began feeling happier. He explains why.
[1] Let me tell you a bit about myself. I’m 35 years old, male, single, never been married. I work as an
editor at a publishing company. I recently moved from the Nakameguro neighbourhood in Tokyo, where I
lived for a decade, to a neighbourhood called Fudomae in a different part of town. The rent is cheaper, but
the move pretty much wiped out my savings.
[5] Some of you may think that I’m a loser: an unmarried adult with not much money. The old me would
have been way too embarrassed to admit all this. I was filled with useless pride. But I honestly don’t care
about things like that any more. The reason is very simple: I’m perfectly happy just as I am. The reason? I got
rid of most of my material possessions.
Minimalism is a lifestyle in which you reduce your possessions to the least possible. Living with only
[10] the bare essentials has not only provided superficial benefits such as the pleasure of a tidy room or the
simple ease of cleaning, it has also led to a more fundamental shift. It’s given me a chance to think about
what it really means to be happy.
We think that the more we have, the happier we will be. We never know what tomorrow might bring, so
we collect and save as much as we can. This means we need a lot of money, so we gradually start judging
[15] people by how much money they have. You convince yourself that you need to make a lot of money so you
don’t miss out on success. And for you to make money, you need everyone else to spend their money. And
so it goes.
So I said goodbye to a lot of things, many of which I’d had for years. And yet now I live each day with a
happier spirit. I feel more content now than I ever did in the past.
[20] I wasn’t always a minimalist. I used to buy a lot of things, believing that all those possessions would
increase my self-worth and lead to a happier life. I loved collecting a lot of useless stuff, and I couldn’t throw
anything away. I was a natural hoarder of knick-knacks that I thought made me an interesting person.
At the same time, though, I was always comparing myself with other people who had more or better
things, which often made me miserable. I couldn’t focus on anything, and I was always wasting time. Alcohol
[25] was my escape, and I didn’t treat women fairly. I didn’t try to change; I thought this was all just part of who I
was, and I deserved to be unhappy.
My apartment wasn’t horribly messy; if my girlfriend was coming over for the weekend, I could do
enough tidying up to make it look presentable. On a usual day, however, there were books stacked
everywhere because there wasn’t enough room on my bookshelves. Most I had thumbed through once or
[30] twice, thinking that I would read them when I had the time.
The closet was crammed with what used to be my favourite clothes, most of which I’d only worn a few
times. The room was filled with all the things I’d taken up as hobbies and then gotten tired of. A guitar and
amplifier, covered with dust. Conversational English workbooks I’d planned to study once I had more free
time. Even a fabulous antique camera, which of course I had never once put a roll of film in.
[35] It may sound as if I’m exaggerating when I say I started to become a new person. Someone said to
me: “All you did is throw things away,” which is true. But by having fewer things around, I’ve started feeling
happier each day. I’m slowly beginning to understand what happiness is.
[38] If you are anything like I used to be – miserable, constantly comparing yourself with others, or just
believing your life sucks – I think you should try saying goodbye to some of your things. […] Everyone wants
to be happy. But trying to buy happiness only makes us happy for a little while.
Fonte: adaptado de . Acesso em: 21 mai. 2017.
De acordo com o texto, Fumio
GOODBYE THINGS, HELLO MINIMALISM: CAN LIVING WITH LESS MAKE YOU HAPPIER?
Fumio Sasaki owns a roll-up mattress, three shirts and four pairs of socks. After deciding to scorn possessions, he began feeling happier. He explains why.
[1] Let me tell you a bit about myself. I’m 35 years old, male, single, never been married. I work as an
editor at a publishing company. I recently moved from the Nakameguro neighbourhood in Tokyo, where I
lived for a decade, to a neighbourhood called Fudomae in a different part of town. The rent is cheaper, but
the move pretty much wiped out my savings.
[5] Some of you may think that I’m a loser: an unmarried adult with not much money. The old me would
have been way too embarrassed to admit all this. I was filled with useless pride. But I honestly don’t care
about things like that any more. The reason is very simple: I’m perfectly happy just as I am. The reason? I got
rid of most of my material possessions.
Minimalism is a lifestyle in which you reduce your possessions to the least possible. Living with only
[10] the bare essentials has not only provided superficial benefits such as the pleasure of a tidy room or the
simple ease of cleaning, it has also led to a more fundamental shift. It’s given me a chance to think about
what it really means to be happy.
We think that the more we have, the happier we will be. We never know what tomorrow might bring, so
we collect and save as much as we can. This means we need a lot of money, so we gradually start judging
[15] people by how much money they have. You convince yourself that you need to make a lot of money so you
don’t miss out on success. And for you to make money, you need everyone else to spend their money. And
so it goes.
So I said goodbye to a lot of things, many of which I’d had for years. And yet now I live each day with a
happier spirit. I feel more content now than I ever did in the past.
[20] I wasn’t always a minimalist. I used to buy a lot of things, believing that all those possessions would
increase my self-worth and lead to a happier life. I loved collecting a lot of useless stuff, and I couldn’t throw
anything away. I was a natural hoarder of knick-knacks that I thought made me an interesting person.
At the same time, though, I was always comparing myself with other people who had more or better
things, which often made me miserable. I couldn’t focus on anything, and I was always wasting time. Alcohol
[25] was my escape, and I didn’t treat women fairly. I didn’t try to change; I thought this was all just part of who I
was, and I deserved to be unhappy.
My apartment wasn’t horribly messy; if my girlfriend was coming over for the weekend, I could do
enough tidying up to make it look presentable. On a usual day, however, there were books stacked
everywhere because there wasn’t enough room on my bookshelves. Most I had thumbed through once or
[30] twice, thinking that I would read them when I had the time.
The closet was crammed with what used to be my favourite clothes, most of which I’d only worn a few
times. The room was filled with all the things I’d taken up as hobbies and then gotten tired of. A guitar and
amplifier, covered with dust. Conversational English workbooks I’d planned to study once I had more free
time. Even a fabulous antique camera, which of course I had never once put a roll of film in.
[35] It may sound as if I’m exaggerating when I say I started to become a new person. Someone said to
me: “All you did is throw things away,” which is true. But by having fewer things around, I’ve started feeling
happier each day. I’m slowly beginning to understand what happiness is.
[38] If you are anything like I used to be – miserable, constantly comparing yourself with others, or just
believing your life sucks – I think you should try saying goodbye to some of your things. […] Everyone wants
to be happy. But trying to buy happiness only makes us happy for a little while.
Fonte: adaptado de . Acesso em: 21 mai. 2017.
Antes da mudança, Fumio acumulava bens materiais porque
Se x é um número real que satisfaz x3 = x + 2, então x10 é igual a