(UECE) Se V é uma matriz quadrada e n é um número natural maior do que um, define-se Vⁿ = V . V^n-1. Com essa definição, para a matriz  pode-se afirmar corretamente que o valor do determinante da matriz y = V + V² + V³ + ... + V²⁰¹⁶ é igual a:

(AFA) THE RELATIONSHIP BETWEEN FRIENDS AND TYPES OF FRIENDSHIP

Everyone has at least one best friend, some maybe even more. There are also those people who are just friends and also arch-enemies. People may think that just because they are your friends it means that they are your best friend. The thing is, even though they are your friend, the relationship between a best friend and a friend is different. Either way regardless of archenemies, friends or best friends, there are not many ways to compare any of these different types of friends, but you can easily contrast them from one another.

Arch-enemies often know more about each other than two friends. In a comparison of personal relationships, ¹friendship is considered to be closer than association, although a wide range of degrees of intimacy exists in friendships, arch-enemies, and associations. Friendship and association can be thought of as spanning across the same continuum. ²The study of friendship is included in the fields of sociology, social psychology, anthropology, philosophy, and zoology. Even animals have familiars! Various academic theories of friendship have been proposed, among which are social exchange theory, equity theory, relational dialectics, and attachment styles. ³In Russia, one typically bestows very few people the status of “friend”.

These friendships, however, make up in intensity what they lack in number. Friends are entitled to call each other by their first names alone, and to use diminutives. A customary example of polite behavior is addressing "acquaintances" by full first name plus their patronymic. These could include relationships which elsewhere would be qualified as real friendships, such as workplace relationships of long standing, or neighbors with whom one shares an occasional meal or a social drink with.

Also in the Middle East and Central Asia, male friendships, while less restricted than in Russia, tend to be reserved and respectable in nature. They may use nicknames and diminutive forms of their first names. In countries like India, it is believed in some parts that friendship is a form of respect, not born out of fear or superiority. Friends are people who are equal in most standards, but still respect each other regardless of their attributes or shortcomings. Most of the countries previously mentioned (Russia, Asia, and even the Middle East) and even our own nation are suffering a decline in genuine friendships.

According to a study documented in the June 2006 issue of the Journal American Sociological Review, Americans are thought to be suffering a loss in the quality and quantity of close friendships since at least 1985. The study’s results state that twenty-five percent of ⁴Americans have no close confidants, and the average total number of confidants per citizen has dropped from four to two. According to the study, ⁵Americans' dependence on family as a safety net went up from fifty-seven percent to eighty percent; Americans dependence on a partner or spouse went up from five percent to nine percent.

Recent studies have found a link between fewer friendships, especially in quality, and psychological and physiological regression. In the sequence of the emotional development of the individual, friendships come after parental bonding and before the pair bonding engaged in at the approach of maturity. In the intervening period between the end of early childhood and the onset of full adulthood, friendships are often the most important relationships in the emotional life of the adolescent, and are often more intense than relationships experienced later in life.

⁶Unfortunately, making friends seems to trouble many of people. Having no friends can be emotionally damaging for all ages, from young children to full grown adults. A study performed by researchers from Purdue University found that post-secondary-education friendships, college and university last longer than the friendships before it. Children with Asperger syndrome and autism usually have some difficulty forming friendships. ⁷Socially crippling conditions like these are just one way that the social world is so difficult to thrive in. ⁸This does not mean that they are not able to form friendships, however. With time, moderation and proper instruction, they are able to form friendships after realizing their own strengths and weaknesses.

⁹There is a number of theories that attempt to explain the link, including that; Good friends encourage their friends to lead more healthy lifestyles; ¹⁰Good friends encourage their friends to seek help and access services, when needed; ¹¹Good friends enhance their friend’s ¹²coping skills in dealing with illness and other health problems; and/or Good friends actually affect physiological pathways that are protective of health. Regardless of what we think, we can clearly see that there are some ways that friends, best friends and archenemies are the same, but in the end they are clearly more different. ¹³Nonetheless we all have every single type in our lives.

(Adapted from: http://www.ukessays.com/essays/philosophy/therelationship- between-friends-and-types-of-friendship-philosophyessay. php) 

“This does not mean that they are not able to form friendships, however” (reference 8). The option that replaces the highlighted expression is 

Os padrões e a frequência com que as infecções parasitárias, tais como malária e esquistossomose, ocorrem em determinadas localidades dependem de interações complexas entre hospedeiros, parasitas e ambiente. A ação do homem dominando e alterando a natureza pode se constituir em fator de progresso e de melhoria da qualidade de vida, porém, também pode introduzir ou espalhar infecções parasitárias, minimizando ou até inviabilizando os efeitos benéficos sobre o bem-estar da população.

CHIEFF, P.P. Alterações ambientais e infecções parasitárias. Arq. Med. v. 47, n. 1. março de 2002. Adaptado.

Segundo o texto, as alterações ambientais provocadas pela atividade humana influenciam a incidência de infecções, pois

ENEM 2010 2ª APLICAÇÃO) American Idol islâmico

Quem não gosta do Big Brother diz que os reality shows são programas vazios, sem cultura. No mundo árabe, esse problema já foi resolvido: em The Millions’ Poet (“O Poeta dos Milhões”), líder de audiência no golfo pérsico, o prêmio vai para o melhor poeta. O programa, que é transmitido pela Abu Dhabi TV e tem 70 milhões de espectadores, é uma competição entre 48 poetas de 12 países árabes — em que o vencedor leva um prêmio de US$ 1,3 milhão.

Mas lá, como aqui, o realitygera controvérsia. O BBB teve a polêmica dos “coloridos” (grupo em que todos os participantes eram homossexuais). E Millions’ Poetdetonou uma discussão sobre os direitos da mulher no mundo árabe.

GARATTONI, B. O American Idol islâmico. SuperInteressante. Edição 278, maio 2010 (fragmento).

No trecho “Mas lá, como aqui, orealitygera controvérsia”, o termo destacado foi utilizado para estabelecer uma ligação com outro termo presente no texto, isto é, fazer referência ao:

Texto

Las danzas y el fuego

[1]     Si bien algunos autores dudan de que en la Península

Ibérica existiesen danzas regladas con anterioridad a la venida

de los romanos, lo cierto es que Estrabón nos habla de los

[4 ]pueblos celtas y celtíberos diciéndonos que bailaban en el

plenilunio a un Dios sin nombre, y por otra parte, han llegado

a nosotros, aunque algo modificadas, un gran número de

[7 ]danzas, la mayoría de las cuales tiene un marcado carácter

religioso. Se pueden citar como ejemplo: las danzas de

vísperas en Galicia, la danza prima en Asturias, la sardana en

[10] Cataluña, etc. Más tarde, al ser conquistada la Península por

los romanos, el pueblo asimiló las danzas, generalmente

licenciosas, que los conquistadores traían, pero manteniendo

[13] siempre las indígenas. Además de las danzas de carácter

religioso, existía otro tipo de danzas muy importante de carácter

guerrero, de las cuales encontramos muestras por toda la

[16] Península, aunque hubo pueblos, como los cántabros, que casi

no fueron invadidos, en los que se conservaron las tradiciones

de una forma más pura.

Rocío Espada. La danza española (adaptado).

Internet: <www20.gencat.cat>.

Según su forma y uso en el texto,

la oración "Más tarde, al ser conquistada la Península por los romanos" (l.10-11) puede ser rescrita, sin producir alteraciones semánticas o gramaticales en el texto, de la forma siguiente: Más tarde, cuando los romanos habían conquistado la Península.