Questões - ITA 2001 | Gabarito e resoluções

(ITA - 2001 - 1a Fase) O nmero complexo , tem argumento. Neste caso, a igual a:

(ITA - 2001) Um tringulo tem lados medindo 3, 4 e 5 centmetros. A partir dele, constri-se uma sequncia de tringulos do seguinte modo: os pontos mdios dos lados de um tringulo so os vrtices do seguinte. Dentre as alternativas abaixo, o valor em centmetros quadrados que est mais prximo da soma das reas dos 78 primeiros tringulos assim construdos, incluindo o tringulo inicial, :

(ITA - 2001 - 1a Fase) In April we asked our readers: is there humor in the workplace? Perhaps engineering is too serious to be funny - or is it? Here is one response: ENGINEER IN HELL To the editor: An engineer dies and reports to the pearly gates. St. Peter checks his dossier and says, Ah, youre an engineer -youre in the wrong place. So the engineer reports to the gates of hell and is let in. Pretty soon, the engineer gets dissatisfied with the level of comfort in hell, and starts designing and building improvements. After a while, theyve got air conditioning and flush toilets and escalators, and the engineer is a pretty popular guy. One day St. Peter calls Satan up on the telephone and says with a sneer, So, hows it going down there in hell? Satan replies,Hey, things are going great! Weve got air conditioning and flush toilets and escalators, and theres no telling what this engineer is going to come up with next. St. Peter replies, What? Youve got an engineer? Thats a mistake -he should never have gotten down there; send him up here.Satan says, No way. I like having an engineer on the staff, and Im keeping him. St Peter says, Send him back up here or Ill sue. Satan laughs uproariously and answers, Yeah, right. And just where are YOU going to get a lawyer? H.D. Mt Vernon, Iowa, USA Considere as afirmaes abaixo: I. So Pedro telefonou ao Diabo para obter informaes sobre o comportamento do engenheiro no inferno. II. O dia-a-dia no inferno tornou-se muito melhor aps a chegada do engenheiro. III. So Pedro ameaou mover uma ao judicial contra o Diabo caso ele desprezasse os servios do engenheiro. Est(o) condizente(s) com o texto:

(ITA - 2001) Considere as afirmaes abaixo relativas concentrao (mol/L) das espcies qumicas presentes no ponto de equivalncia da titulao de um cido forte (do tipo HA) com uma base forte (do tipo BOH): I. A concentrao do nion A- igual concentrao do ction B+ II.A concentrao do ction H+ igual constante de dissociao do cido HA. III.A concentrao do ction H+ consumido igual concentrao inicial do cido HA. IV.A concentrao do ction H+ igual concentrao do nion A- V.A concentrao do ction H+ igual concentrao do ction B+ Das afirmaes feitas, esto CORRETAS

(ITA - 2001 - 1a Fase) No sistema convencional de trao de bicicletas, o ciclista impele os pedais, cujo eixo movimenta a roda dentada (coroa) a ele solidria. Esta, por sua vez, aciona a corrente responsvel pela transmisso do movimento a outra roda dentada (catraca), acoplada ao eixo traseiro da bicicleta. Considere agora um sistema duplo de trao, com 2 coroas, de raios R1 e R2 (R1 R2) e 2 catracas R3 e R4 (R3 R4 ), respectivamente. Obviamente, a corrente s toca uma coroa e uma catraca de cada vez, conforme o comando da alavanca de cmbio. A combinao que permite mxima velocidade da bicicleta, para uma velocidade angular dos pedais fixa,

(ITA - 2001 - 1a Fase) Em um farol de sinalizao, o feixe de luz est acoplado a um mecanismo rotativo que realiza uma volta completa a cada T segundos. O farol se encontra a uma distncia R do centro de uma praia de comprimento 2L, conforme a figura. O tempo necessrio para o feixe de luz varrer a praia, em cada volta,

(ITA - 2001 - 1a Fase) In April we asked our readers: is there humor in the workplace? Perhaps engineering is too serious to be funny - or is it? Here is one response: ENGINEER IN HELL To the editor: An engineer dies and reports to the pearly gates. St. Peter checks his dossier and says, Ah, youre an engineer -youre in the wrong place. So the engineer reports to the gates of hell and is let in. Pretty soon, the engineer gets dissatisfied with the level of comfort in hell, and starts designing and building improvements. After a while, theyve got air conditioning and flush toilets and escalators, and the engineer is a pretty popular guy. One day St. Peter calls Satan up on the telephone and says with a sneer, So, hows it going down there in hell? Satan replies,Hey, things are going great! Weve got air conditioning and flush toilets and escalators, and theres no telling what this engineer is going to come up with next. St. Peter replies, What? Youve got an engineer? Thats a mistake -he should never have gotten down there; send him up here.Satan says, No way. I like having an engineer on the staff, and Im keeping him. St Peter says, Send him back up here or Ill sue. Satan laughs uproariously and answers, Yeah, right. And just where are YOU going to get a lawyer? H.D. Mt Vernon, Iowa, USA Ao afirmar ... and theres no telling what this engineer is going to come up with next., o Diabo quer dizer que:

(ITA - 2001 - 1a Fase) Sabendo que de 1024 a soma dos coeficientes do polinmio em x e y, obtido pelo desenvolvimento do binmio (x+y)n, temos que o nmero de arranjos sem repetio de n elementos, tomados 2 a 2, :

(ITA - 2001) Quando carbeto de alumnio (A4C3) adicionado em um bquer contendo gua lquida a 25C, ocorre a formao de hidrxido de alumnio e a liberao de um gs. O gs formado o

(ITA - 2001 - 1a Fase) A respeito das combinaes mostradas abaixo, temos que, para cada n = 1, 2, 3, ..., a diferena an - bn igual a: e

(ITA - 2001 - 1a Fase) In April we asked our readers: is there humor in the workplace? Perhaps engineering is too serious to be funny - or is it? Here is one response: ENGINEER IN HELL To the editor: An engineer dies and reports to the pearly gates. St. Peter checks his dossier and says, Ah, youre an engineer -youre in the wrong place. So the engineer reports to the gates of hell and is let in. Pretty soon, the engineer gets dissatisfied with the level of comfort in hell, and starts designing and building improvements. After a while, theyve got air conditioning and flush toilets and escalators, and the engineer is a pretty popular guy. One day St. Peter calls Satan up on the telephone and says with a sneer, So, hows it going down there in hell? Satan replies,Hey, things are going great! Weve got air conditioning and flush toilets and escalators, and theres no telling what this engineer is going to come up with next. St. Peter replies, What? Youve got an engineer? Thats a mistake -he should never have gotten down there; send him up here.Satan says, No way. I like having an engineer on the staff, and Im keeping him. St Peter says, Send him back up here or Ill sue. Satan laughs uproariously and answers, Yeah, right. And just where are YOU going to get a lawyer? H.D. Mt Vernon, Iowa, USA Quais frases, numeradas de I a IV, teriam o significado mais prximo a Send him back up here or Ill sue, que se encontra no penltimo pargrafo do texto? I. If you dont send him back up here, Ill sue. II. If you send him back up here, Ill sue. III. Unless you send him back up here, I wont sue. IV. I will sue, unless you send him back up here.

(ITA - 2001) Considere as seguintes afirmaes relativas a reaes qumicas ocorrendo sob as mesmas temperatura e presso e mantidas constantes. I. Uma reao qumica realizada com a adio de um catalisador denominada heterognea se existir uma superfcie de contato visvel entre os reagentes e o catalisador. II. A ordem de qualquer reao qumica em relao concentrao do catalisador igual a zero. III. A constante de equilbrio de uma reao qumica realizada com a adio de um catalisador tem valor numrico maior do que o da reao no catalisada. IV. A lei de velocidade de uma reao qumica realizada com a adio de um catalisador, mantidas constantes as concentraes dos demais reagentes, igual quela da mesma reao no catalisada. V. Um dos produtos de uma reao qumica pode ser o catalisador desta mesma reao. Das afirmaes feitas, esto CORRETAS

(ITA - 2001 - 1a Fase) Uma bola lanada horizontalmente do alto de um edifcio, tocando o solo decorridos aproximadamente 2s. Sendo de 2,5m a altura de cada andar, o nmero de andares do edifcio

(ITA - 2001 - 1a Fase) TV CRITIQUE Amid the majestic sequoias of what could be a state park in Northern California, the silence is broken by a guttural bellow. An enormous beast plods across the television screen. She kicks out a shallow nest and begins to lay her eggs. Each white egg, the size of a soccer ball, slides gently down an ovipositor and comes to rest in the ground. (...) It looks and sounds just like a wildlife documentary -so much so that, if you watch long enough, you almost forget that the animals it shows have been extinct for more than 65 million years. But this is Walking With Dinosaurs, a sometimes stunning dinoextravaganza that uses computer animation and detailed puppets to resurrect the creatures and place them in real landscapes. When the $10 million program aired in the United Kingdom last fall, 17 million people -almost a third of the population -tuned in to the six weekly installments making it the BBCs most watched science program ever and one of its top 20 programs of all time. It also stirred up a controversy. Some researchers were unstinting in their praise: This is going to stand out as one of the best dinosaur shows ever done and certainly the most novel one,says Tom Holtz, a vertebrate paleontologist at the University of Maryland, College Park, who consulted with the BBC on the project. But others cringed at the way it blurred fact and fiction. Most of the egg-laying sequence, for example, is screenwriters fantasy: There is no scientific evidence that the giant dinosaur Diplodocus had an ovipositor or abandoned its young. Some of the arguments were just so far-fetched, so ridiculous,says Norman MacLeod, an invertebrate paleontologist at the Natural History Museum in London. I was embarrassed for the profession.The British media debated whether docudrama was a suitable way to convey science to the public. Would TV viewers be stimulated, misled, or just confused? On 16 April millions more will get the chance to make up their own minds as the Discovery Channel airs a revised 3-hour version of the show in North and South America. (...) SCIENCE VOL 288 7 APRIL 2000 Considere as afirmaes abaixo: I. O primeiro pargrafo do texto descreve uma cena do documentrio Caminhando com Dinossauros, em que um dinossauro prepara seu ninho e pe ovos. II. O documentrio, dividido em seis episdios semanais, estreou na Inglaterra no outono de 1999. III. Em abril deste ano, o canal de televiso Discovery transmitiria para os Estados Unidos e para a Amrica do Sul o documentrio britnico na ntegra. Est(o) condizente(s) com o texto:

(ITA -2001 - 1a Fase) Em um bquer, contendo uma soluo aquosa 1,00mol/L em nitrato de prata, foiadicionada uma soluo aquosa contendo um sal de cloreto (MyClx). A mistura resultante foiagitada, filtrada e secada, gerando 71,7 gramas de precipitado. Considerando que no tenharestado cloreto no lquido sobrenadante, o nmero de mols de ons Mx+ adicionado mistura,em funo de x e y, Dados:Massa molar do AgCl= 143,32 g/mol