（3）がなぜこの答えになるのか理解できません解説よろしくお願い致します🙇🏻‍♀️💦

5 下の図は自転車についている発電機である。 なさい。 M ある位置で A thy) B A ← R SN B 問いに答え が静止した。 (a) b 1) 発電機の磁石を回転させ,電球を点灯させた。このように、コイルの中の磁界を 変化させることによって,コイルに電圧が生じる現象を何というか。誘導 2) コイルの中の磁界が最も強くなるのはどれか。 ② 〜Cの中から選び、 記号で答え なさい。 (3)右回りに回転している磁石が~の位置にあるとき,電流の向きはそれぞれ図 のどの向きになるか。 次のア~ウの中から選び、記号で答えなさい。 ア Aの向き イB の向き ウ 電流は流れない。 (4) 自転車の発電機に生じる電流は,直流,交流のどちらか。 ・テ ウイ P F 電球を点灯させながら乗っていると、電球が切れてしまった。そのときどのよう になるか。次のア~オの中から2つ選び、記号で答えなさい。 アペダルを踏む力が小さくてすむ。 イペダルを踏む力は変わらない。 ウペダルを踏む力が大きくなる。 エ 発電機の電圧は生じなくなる。 アオ オ 発電機の電圧は生じているが, 電流は流れない。ま > ** と長さ の位置 電子 T

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3 次の英文を読み, 空所に入れるのに最も適切なものを, それぞれ下の①~④のうちから一つずつ選びなさい。 Cigarette smoking has negative effects not only on the body of the person who smokes but also on the body of someone who regularly breathes in second-hand smoke. Some of the most obvious effects are high blood pressure, sleep disorders, heart failure, and lung cancer. Despite such harmful consequences, ( 10 ). It has been reported that smoking creates feelings of pleasure, reduces tension, and promotes close relationships. Many smokers admit that smoking is a bad habit. ( 11 ), they tend to think that the number of cigarettes that they smoke is below the danger level and thus are not worried about the risk. Some even feel that they do not breathe in the smoke and that a cure for cancer will be found before they become ill with the disease. We have to admit that smoking is a habit which is difficult to break ( 12 ) the nicotine found in tobacco goes into the blood and stimulates the brain, making smokers feel pleasant for several minutes. What is more, the smoker usually feels anxious and wants to have another cigarette. ( 13 ) the policies that now ban smoking in most public areas, the stress that people often experience at work and at home can force them to smoke. ( 10 ) ①some people decide to stop smoking millions of people continue to smoke ( 11 ) the price of cigarettes has risen ①smoking is more harmful than drinking Therefore 2 While ③ Of course 4 However (12) 1 because 2 as a result 3 but SO (13) ①Despite 2 Although (3) But 4 Yet

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2 次の英文を読み, 空所に入れるのに最も適切なものを,それぞれ下の①~④のうちから一つずつ選びなさい。 (6) When growing tomatoes, we know we should pick them when they're bright red. With carrots, however, ( 6 ) because they grow underground. ①we should pick them when they turn orange (2) it's hard to know when they're ready (3) we should grow them more carefully than tomatoes (4) it's easy to know when they're bright red (7) Although it is quick, easy and convenient to be able to look up information on the internet, it can sometimes be difficult ( 7 ) because there is so much information. to find what you are looking for (2) to improve the convenience of the internet (3) to get more than what you need that people often experie (4) to have good computer literacy (8) Would you be happier if you were richer? Many people believe that they would be. But research conducted over many years suggests that ( 8 ). People in the United States, for example, are, on average, richer than New Zealanders, but they are not happier. poorer people tend to worry about their financial problems 2 pleasure in life usually comes from great wealth (3) the best way to be happy is learning how to save money greater wealth doesn't generally imply greater happiness (9) Many European rivers were once heavily polluted by manufacturing industries. As a result, wild animals dependent on clean water disappeared. However, as stricter environmental standards took effect, rivers such as the Thames of London have become much cleaner. Consequently, ( 9 ). water quality has continued to decline wild animals avoid drinking from the Thames (3) wild animals are making a comeback in many rivers (4) wild animals no longer depend on clean water

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1 次の各英文で,空所に入れるのに最も適切なものを,それぞれ下の①~④のうちから一つずつ選びなさい。 (1) It is true that training helps improve performance, ( ) there must be some limit to how fast a person can run. 1 as ( SO ③ but because ) we didn't arrive on time, we were not allowed to enter the lecture hall. ①Because Although (3) Therefore However (3) Sunlight produces vitamin D in our bodies, which is necessary for good health. ( ), doctors tell us that spending too much time in the sun can result in skin cancer. ①Because 2 Thus 3 Suppose ④However (4) People have been using white vinegar as a natural alternative to chemical treatments, ( A ) it can lower blood sugar, kill bacteria, and help treat insect bites. ( B ), these benefits might come with some risk. Vinegar's acid can also damage your stomach, throat, and teeth. ①A: since B: Therefore 3 A: though B: However 2 A though 4 A: since B: Therefore B: However (5) We were planning to travel abroad this summer, ( A ) we ended up staying home ( B ) we were both too busy. A while B: so 2 A: but B: because (3) A: so B: though 4 A: since B: but

多様体を構成するために、位相空間に完全アトラスを導入するところで質問です。 完全アトラスを導入するメリットとして、この文章の下線部を「異なる座標系を用いたのに同じ計算ができてしまうという問題が解消される」解釈したのですが、そこがよくわかりません。座標系を変えて計算する... Read More

1 Two n-dimensional coordinate systems & and ŋ in S overlap smoothly provided the functions on¯¹ and ŋo §¯¹ are both smooth. Explicitly, if : U → R" and ŋ: R", then ŋ 1 is defined on the open set ε (ur) → ° (UV) V and carries it to n(u)—while its inverse function § 4-1 runs in the opposite direction (see Figure 1). These functions are then required to be smooth in the usual Euclidean sense defined above. This condition is con- sidered to hold trivially if u and do not meet. Č (UV) R" Ĕ(U) n(UV) R" S n(v) Figure 1. 1. Definition. An atlas A of dimension n on a space S is a collection of n-dimensional coordinate systems in S such that (A1) each point of S is contained in the domain of some coordinate system in, and (A2) any two coordinate systems in ✅ overlap smoothly. An atlas on S makes it possible to do calculus consistently on all of S. But different atlases may produce the same calculus, a technical difficulty eliminated as follows. Call an atlas Con S complete if C contains each co- ordinate system in S that overlaps smoothly with every coordinate system in C. 2. Lemma. Each atlas ✅ on S is contained in a unique complete atlas. Proof. If has dimension n, let A' be the set of all n-dimensional coordinate systems in S that overlap smoothly with every one contained in A. (a) A' is an atlas (of the same dimension as ✅).

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13 次の日本文にあう英文になるように, □(1) 眠気を感じて, 私は草の上に横になった。 に適する語を書きなさい。 □(2) ロンドンで生まれたので、彼女は英語を流暢に話す。 sleepy, I laid myself on the grass. in London, she speaks English fluently. □(3) 彼女は泳げないので、海が好きではない。 to swim, she doesn't like the sea. ike the sea □ (4) 昨年に比べて,今年は冬の訪れが早い。 Winter has come early I love with last year. □(5) 率直に言えば、私は彼の歌はあまり好きではない。 Frankly door food. other food, I don't like his songs very much. it was totally con 4 次の文中の下線部を ( 内の指示にしたがって書きかえなさい。 □(1) As I have never read the book, I can't criticize it. (分詞構文に) Oine plane □ (2) Properly trained, dogs can do some tricks. (副詞節に) thers, I can't criticize it. dogs can do some tricks. □ (3) Since their conversation was in Chinese, I didn't understand a word. (分詞構文に) を用いて) □ (4) Lost in thought, he didn't notice us. (副詞節に) I didn't understand a word. □ (5) She knelt on the floor, and she closed her eyes. (with を用いて) She knelt on the floor, □ (6) Printed in haste, the book had many misprints. (副詞節に) he didn't notice us. the book had many misprints.

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・次の各組の英文がほぼ同じ内容を表すように, に適する語を書きなさい。 (1) Since Ken was brought up in London, he speaks English fluently. up in London, Ken speaks English fluently. (2) Having read the letter, he kept silent for a long time. After the letter, he kept silent for a long time. (3) As there were a lot of things to do last week, I'm still tired. a lot of things to do last week, I'm still tired. (4) It had kept raining for days, so she couldn't dry clothes. raining for days, she couldn't dry clothes. (5) Emily, having seen the movie twice before, didn't want to see it again. Emily didn't want to see the movie again, seen it twice before. (6) She got lost, because she had left the map behind. She got lost, the map behind. (7) The machine, having been used for many years, still worked well. The machine still worked well, many years. it used for

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2 次の文の( )内の語を適する形になおしなさい。 (1) My father repaired the (break) wall. (2) She came to school without (have) breakfast. (3) The boy looks (please) with magic tricks. (4) Do you know the woman (wait) for a bus? (5) The letter (write) by Meg has just arrived. (6) I couldn't make myself (understand) in Spanish. (2点×6)

この問題で何故1、2は名詞の前がaで3はtheになるのでしょうか？ 特定の物や周知しているもの、既知しているものにはtheを付けその他の数えられる名詞にはa anを付けることは理解しているのですがそれでもわからないので教えて頂きたいです。

次は、 Alex に紹介するものの候補です。 ①〜③の写真から2つを選んで番号を()に書き, 例を参考にして、それを Alex に紹介する英文を書こう。 books ① print festival M ③ movie. 「ノルウェイの森」 著:村上春樹 提供: 講談社 村上春樹が1987年に書いた 葛飾北斎が作っ 「神奈川沖浪裏』 ©浅草神社 多くの人が毎年楽し 例 This is a book that Murakami Haruki wrote in 1987. 多くの人が2019年に見た! 「天気の子 これは村上春樹が1987年 に書いた本です。 ( ① )(例) This is a print that Katsushika Hokusai made. (②) (例) This is a festival that many people enjoy every year. CAN-DO 自己表現のマルつけコーナー 別解1 ② についてほかの表現で紹介している。 別解 3 that を使わ This is a print Ke This is a festival that [which] a lot of (これは葛飾北斎が作っ people go to see. (これは多くの人が見に行く祭りです。) 別解2 ③について紹介している。 This is the movie that [which] many [a lot ofl people saw [watched] in 2019. (これは2019年に多くの人が見た映画です。) This is a festival year. (これは多くの人が毎年 This is the movic saw [watched] in (これは2019年に多くの

(1)の答えがD、(3)の答えがウ、(6)の答えがイ なんですけど、なんでそれになるかと、5⃣で3~5程の段落で分けるとしたらどこになるのか、またその段落はそれぞれどんな題名になるのかを教えて欲しいですm(_ _)m

学院) E J 5 次の英文を読んで、あとの問いに答えなさい。 < 星野改〉 High schools in Minnesota have a problem Many students are late to school. They are often tired. Some students fall asleep in class. They often get sick, too. The local governments take that as a problem. They make a small change.) It helps a school day a little later/ A lot! What do they do? They start the D- This small change makes a big difference. Why? Most teens are very tired early in the morning. They usually don't go to bed until after midnight In the morning, they wake up between 6:00 and 6:30 for school. So they don't get enough sleep! They are still tired early in the morning. But after the change/ teens are more awake and later start time is better for a teen's body clock I be ready/class/to/in). A be in ready class Everyone has a body clock. An adult's body clock works like this: most adults get tired between 9:00 and 11:00 at night. They usually go to bed before midnight. Adults can get up early in the morning. It's not a problem. But a teen's body clock is different. Teens don't get tired at midnight. They usually stay up later. But early in the morning, they need more sleep. B FO C The schools in Minnesota pay attention to the teen's body clock. They change the start of the school day from 7:20 a.m. to 8:40 a.m., 80 minutes later. Other schools in the United States change their start times too. Some schools change the time by only 30 minutes, but they still get good results. ( 2 ), the results are amazing! ③(Many) students are on time. Morning classes are easier to teach. Students are getting ①(good) grades. Students have fewer illnesses, so they are ⑤(little) absent. In Minnesota, there is another important effect: fewer students drop out of school or change schools. D Today, more and more high schools are starting later. Most schools can't start two hours later. But they can change the start time a little. A small change can make a very big difference! Just ask the students. Minnesota ミネソタ (アメリカ合衆国中央北部の州) (1) 次の英文を入れるのに最も適する位置を, 本文中のA~Dから1つ選びなさい。 Now the students are happier, and also the parents and teachers too. D(A) (2)下線部①の ( )内の語を並べかえて正しい英文を作るとき, 3番目にくるものをア~エから1つ選びなさい。 ア be イ ready ウ class I to (3) 20)( )に適するものを, ア~エから1つ選びなさい。 7 On the other hand (4) 3~50)( 1 However ウ In fact I Even so )内の語をそれぞれ比較級にかえなさい。 (3) much (5)本文の内容にあうものを,ア~エから1つ選びなさい。 more (T!) better ⑤⑤ fewer Less High school students in Minnesota are always taking classes seriously. Most teens usually go to bed as early as possible. Most adults don't stay up late because of their body clocks. I Some schools changed the school time but their students did not have good grades. 本文のタイトルとして最も適するものを,ア~エから1つ選びなさい。 7 Fewer Illnesses 1 Late Start Body Clock I Good Sleep イ (土)