大学 幾何学 専門の方からすると基本問題と伺ったのですが、私が文系大学生ということもあり、何も解答を出せません。 解答を出していただけますと幸いです。 3題のうち１題だけでもとても嬉しいです。 よろしくお願いいたします。

1. S2 = {(x,y,z) ∈ R3 | x2 + 42 + 22 = 1} を単位球面とし, R3 のry平面を自然に R2 と同一 視する: {(x, y,0) | (x, y) = R²} ↔ R², (x, y,0) ↔ (x, y). “北極” (0,0,1) 以外の各点 p∈ S2 に対し, p と (0,0,1) を結ぶ直線と xy平面との交点を n(p) とすることで 写像 ゆN: S2\{(0,0,1)} → R2 が定まる. これを北極からの立体射影とよぶ.同様に,p∈ S2\{(0,0,-1)} と “南極” (0,0,-1) を結ぶ直線を考えることで, 南極からの立体射影 $s: S2 \{(0,0,-1)} → R? ができる.これらにより与えられる球面の二つの“地図”(局所座標)の間の変換 son²を 考えよう.この座標変換の定義域 (すなわち ♀N の行き先の R2 の中の適当な開集合) 上の 座標軸に平行な直線たち Lk={(x,k)|n∈R}, L'k={(k,y)|y∈R}(k= -2,-1,0,1,2) (下の図を参照) を pson でうつしてできる曲線の絵を描け. L2 L1 Lo L_1 L-2 I'_2I'_L' LL'2 son の式を計算して求めても、 作図によって求めても良い. 答えだけではなく, 理由も (読み手が理解できるように) 説明すること.

2段落4行目の enjoyed はここではどういう意味ですか？ 訳の分からして、鑑賞する でいいのでしょうか？

意図される there is a really powerful and growing 去る 0FP8 美術作品 which leaves no waste behind 2 for example People spend hours creating amazing artworks in sculpturs, the sand. Sand sculpture competitions are held on beaches all around the world. These amazing, complex art forms which can even be five meters tall and take days to build, 複雑な Am 18 are enjoyed for a short time before they just become part of the beach again. Some artists create *edible art, such as decorated cakes (or chocolate sculptures As though many people take videos or [2] 下線部 雨で非 [3] What comp Some it is [4] 以下 The

中3　三平方の定理 青い三角形を求めます、4cmを底辺として面積を求めたい時、なぜxが高さになるのですか？

20:35 ホーム 確実に正解したい。 定番問題 ① 4cm 120° 面積は? x=6x²/ 2 6cmcm XC =3√3 4x313x 1/1/2 =6.3cm² 2828282 @sakapon2023 チャンネル登録 確実に解きたい定番問題わかる? オリジナルの音声 83 (+) ショート all 75 2 登録チャンネル 793 低く評価 日 12 共有 リ･･･クス マイページ

この問題について、答えは①ですが③ではいけない理由を教えてください🙏

10000 10 I IS NOTung Listen! I ( 1 hear Power Up! 3 ) a funny noise outside. 3 have heard ④ was hearing 1903 j 進行形にできない動詞 (『状態』を表す動詞) を表す動詞 Jam hearing

下から5行目のit would～の文構造がわからないです。back upはどのような働きをしているのでしょうか。 教えて頂けるとありがたいです。

A Makeover for Hoover Dam Hydropower has attracted increasing attention in recent years as a renewable type of clean energy. As long as a suitable water source is available, hydropower facilities are usually good investments, producing energy in a manner that generates far less air pollution and CO2 emissions than fossil fuels do. The most common way to generate hydropower is to trap water at a high elevation behind a dam so it can be released and used to spin turbines below, which, in turn, power electricity-producing generators. However, hydropower has its drawbacks. Droughts and increased water consumption have reduced the flow of many rivers. As rivers become shallower, the necessary volume of water for electricity difficult to maintain, and power supply and generation is dependability are negatively impacted. more Variability in water levels has particularly affected Hoover Dam, a mega-scale hydropower facility in the US state of Nevada. Built in the 1930s at enormous expense to control the frequently flooding Colorado River and maintain a water supply for farmland irrigation, the dam's hydropower capabilities were seen as a way to recover some of the costs of its construction over the long term. The dam's electricity-generating capacity, however, was challenged from the start by seasonal variability in water flow, and in recent years has been greatly reduced by droughts. Combining hydropower with other alternative energy sources, though, may offer a solution. Solar and wind plants can produce enormous amounts of electricity, but one serious downside is that the energy they produce is not available when there is little sun or wind. While conventional batteries can help with this issue, storing such tremendous volumes of electricity has long been a challenge. A recently proposed system for Hoover Dam could provide an answer, though. The plan suggests building a new pumping station that would be powered by both wind and solar. It would push water from the river back up to Hoover Dam, refilling the lake behind it. The water could be released anytime to power the dam's generators in order to reliably meet demand for electricity. Kelly Sanders, an engineering professor at the University of Southern California, is enthusiastic about the storage plan, saying, "We by the p replace fo solat als are st ons to the What is 1 Inst inves 2 WE dams 3 A neg sys 1 en

この文法事項が見えないです

8 紫色のもと [文化] (114 words) 7.1 1.2 1.3 CO (= won 6 語句 has often been regarded as ~ ｢しばしば~とみなされてきた」 : regard Aas B で 「AをBとみなす」 の意味。 which is の省略 the dye [(whichis) used to produce it] S did not have an elegant beginning 長い主語に注意/同格を表すカンマ An ancient people S = the color purple <living along the coast of the Mediterranean Sea> 現在分詞の後置修飾 first discovered V [how to make the dye from Murex snails, O 同格 || small sea animals with hard shells]. B

クロスワードのレベルが高すぎて私には全く解けません。クロスワードのコツとかも教えて欲しいです

(Build Up Your Vocabulary DIRECTIONS First, complete the crossword by reading the clues below (all the answers are words used in the Main Reading). Then, reorder the letters placed and you'll find a key term in the Main Reading. in Down C Across 3. the larger group within a society 4. to include something 7. to get something T Y KEY TERM: L 6 E H L group of people 3. the smaller group within a society 5. a country that is strong and has a lot of influence 6. the thing that allows something to be expressed y W 4 1. relating to politics 2. a system of communication by written or spoken words that is used by a particular E ISM

答えはBです。 後者ははアメリカ英語を学習した人にとってはなじみがある。 従って/言い換えると、両方とも正しい英語である。 変ですか？ CとDがおかしい理由教えてください。

The latter may be more familiar to those The former is common in who have learned American English. Why did this happen? Noah Webster, a textbook author and Great Britain, Canada and Australia. lexicographer, wanted "Americanized" spelling and pronunciation of words, different from those in Great In 1828, he published a two-volume dictionary which greatly helped to make the Americanized Britain. spelling common. The fact of the matter was it was part of American nationalism. After winning political from Great Britain in 1776, Americans became more conscious of developing their own identity as a new In literature, Americans rejected such European criticism nation. Nationalism rose in various fields. The northeastern region produced world-famous American as "Americans have no national literature." Which is more familiar to you, "centre" or "center"? writers I Edgar Allan Poe, a detective story writer and Ralph Waldo Emerson. In addition to these writers, there were also inventors who greatly helped in advancing American industry. Cyrus Hall McCormick, the inventor of the reaper, and Samuel F. S. Morse, the developer of the telegram code, are two such inventors. 間 1 In diplomacy, President James Monroe issued in 1823 the so-called "Monroe Doctrine," a warning to European nations not to interfere with America and the Western Hemisphere. It was the American This policy of isolationism embraced in the doctrine continued as the U.S. intention to be オ diplomatic policy until the end of the century. While challenging European criticism and power, young America tried to be more independent of Europe, not only politically, but economically, culturally and diplomatically. (2) lexicographer: ##*** isolationism: ŽÈ* ア both are correct English. 33 空所 A In addition reaper: 刈り取り機 interfere 干渉する Brajcich and Tanioka (2010) Eye on American Culture (**) ***** ア を満たすのに最も適切なものを、A~Dのうちから1つ選べ。 B However C Therefore D In other words

大学受験の英文法の過去問題なのですが、回答がありません。どなたか答えてくれると助かります！

問題 1 1 選び, 記号で答えなさい。 (*のついた語には語注がある。) editorial column: A daily newspaper cannot publish for 200 years without things wrong. The most serious mistakes stem but from the editorial column 1.7 being gotten 1 get 2. ア only release: 3 12 3. ア who calls I who called に入る最も適切なものをア~オからそれぞれ1つ 4. ア be pardon I be pardoned being got 1 called Kathleen was put in prison for murder, 3 by the media as the 4 In a letter requesting Kathleen country's "most hated woman." released*, scientists say her children died of natural causes. and (The Washington Post, calling some 2 from the news pages ( The Guardian, —) never I not 1 pardoning. gone pardon I getting have gotten nonetheless without calling which pardons 0150610 7)

4番の書き直しの答え教えてください🙇‍♀️

He studied maps, made maps of his own voyages and of the voyages of others, and read books of travel. And always he said to himself: "There is an ocean east of China and an ocean west of Europe. Well, if the earth is round, it must be the same ocean that reaches from Europe around to China and laps the shores of both. And anyone can see that the earth is round if he watches how a ship sails out of sight on a clear day. Its hull disappears first, then the sails, till at last the very tip of the mast drops out of sight over the curve of the sea. If I could sail westward far enough, I know I should reach the eastern lands, and the great prob- lem would be solved." But Columbus had no way of proving his belief that he could get to the East by sailing (©). He was a poor man, and he had no money of his own with which he could buy ships, pay for supplies, and hire sailors to prove his kings and queens were rich () and powerful () in the belief. Only days to *fur- nish what he needed. For many long years (toto / helend / get / tried him/ships and sailors / one or another of the kings of Europe) with which to make the voyage. Of the great countries only France remained, and Columbus determined to go there. If the king of France failed him, no hope was left. *hull : 「船体」 *furnish: 「~を提供する」 C ships 1) 文中の空所ⓢⓔ (2ヵ所ある)に適語を1話ずつ補え, (各3) 2) 下線部の不定詞に用法の点で最も近い不定詞を含む文を次から1つ選び, 記号で答え £. (3) a b Cin It is difficult to finish it within a week. She was happy to receive. a love letter. You must work hard to master math. d She must be mad to say such a thing. 3) カッコ ⓘ が 「彼はヨーロッパの国王に誰かれとなく船と船員を貸してもらおうと努めま した」 という意味を表すように、 カッコ内の語句を並べ換えよ。 (6) 4) 下線部 ⑧ とほぼ同意になるように、次の書き出しに続けて英文を完成させよ。 (4) Columbus determined that ... 5) 本文の内容と一致するように,次の空所に適切な語を1話ずつ補え。 (各3) 7 Geography was among Columbus's ( ) studies. ). At the age of fourteen, Columbus became a ( The king of France was the (1) hope of Columbus. ( 12:10) を和訳せよ。 6) 下線部 how de P jole sicut to stay at badan dan undhe as.