Felix's parents spoke to French President Emmanuel Macron about his case during a recent state visit to neighbouring Singapore, where the... 続きを読む

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... 続きを読む

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 ✅).

ここが分かりません誰か教えてください。

がく Aにちの 長文 キャンプ1日目! 自然に囲まれて 冒頭でつかむ! ストーリー Q岳, エマ, ひな,トムの 4人が行ったのは? The lake. The mountain. トムの日記を読んで、 問いに対する答えの _に適する語を書きましょう。 Summer Camp, Day 1 <6点×3 Gaku, Emma, Hina and I went to the summer camp at the lake. We stayed at a lodge for two days. When we got there at eleven o'clock, it was raining. But after lunch, the rain stopped, and we saw a rainbow! It was really beautiful. In the afternoon, Hina and I enjoyed fishing at the lake. Gaku and Emma enjoyed swimming together. It was sunny and hot, so everyone was thirsty. We drank a lot of water. It was cold and very delicious! 〈注〉 rainbow 虹 thirsty のどがかわいた drank drink の過去形 cold 冷たい (1) What time did Tom get to the lake? - ・At He saw a beautiful (2) What did Tom see after lunch? (3) How was the weather in the afternoon? It was sunny and 5 9

わかりません

G [ ]に入る最も適切なものを選びなさい。(4点×3=12点) 1. After the first day at school, Emma happily [ TOY baig to her family. (a) described ] her teacher and classmates od nes ji bas Jil 193 bus out over of Ew longa ai ats fi it is wo wollo ad oved ow lidbooW to go on 12H. (b) approached 2. He gained great [ (c) celebrated (d) judged (d) policy ] but used it mostly to help the poor. won root otro tuo abasit olime toy slet ba (b) courage (c) wealth (a) belief 3. A Is Yuka waiting for the result of her entrance exam? B: Yes. I'm sure she'll pass because she looked very [ (a) familiar (zysbnoM besok (b) formals A eet: allea (c) nervous ]. (d) confident

なぜPrayedがスキーにはないんですか？違いを教えて欲しいです

3 自己表現 スポーツ好きのEmma に, クラスメートのスポーツ経験を教えてあげましょう。 思判・表 Kei テニスを何度も Yuki スキーを2度 Shinji バレーボールを数度 Sidena. タート 左のメモを見て「〜は…したことがあります」 と彼らを Emma に紹介する英文を完成させよう。 ① Kei has (例) played tennis many times. ② Yuki has (例)skied twice uoy avoH - (2)今度は,あなたのスポーツ経験をEmmaに伝える英文を書こう。 (例) I have played table tennis once.

おかしいところがあれば教えてください

met er s d m (2) Increasing the amount of CO₂ in the atmosphere grobal warming (3) Many people read free news free news on PC screen Cause year by year instead of buying newspaper" with the advent of hew media. pow (+) Japan is facing serious problem. That working population which support the lives of retiring people these days. (5) I was worried about that no bread was sold in the supermarket due to almost closing Time, but fontunately one loaf was left.

この問題の（2）に当てはまる最も適当な言葉を選ぶ問題で、 選択肢（ア）planning （イ）visiting （ウ）going （エ）staying の中から選ぶのですが答えは（ウ）でした。 （ア）のplanningではダメなのですか？

1 陽子 (Yoko) と留学生のエマ (Emma) が話しています。 次の対話が成り立つように, 下線部 (1) から (3) までのそれぞれにあてはまる最も適当なものを、 あとのアからエまでの中から選びなさい。 Yoko: I'm going to visit my sister in Australia. (1) I miss her. You went to Sydney last year, didn't you ? Emma: Yes, I visited my aunt. Yoko: Did you go there with your family? Emma: Yes. My aunt took us to many places in Sydney. I liked the zoo the best. Yoko: We're (2) to a zoo in Sydney, too. I want to hold a koala. (3)______. It's prohibited. Emma: Oh, Yoko: How about taking a picture of a koala ? Can I do that? Emma: Of course, you can! (注) prohibit 〜を禁止する

一番下の行の左のinの用法ってなんですか？ 詳しく教えてください。 また、to不定詞ではダメなのか理由付きで教えてくれると幸いです。！！！(*´ー｀*)

Narges Mohammadi,/ the winner of this year's Nobel Peace Prize,/ may not yet be aware/ she's been recognized for her years of ナルゲス・モハマディ氏は/ 今年(2023年) のノ ーベル平和賞受賞者だが / まだ知らないかもしれ ない / 祖国イランで長年行ってきた人権擁護活動 // というのは/こ により栄誉を受けていることを。 human-rights activism in her native Iran That's because/ the 51-year-old woman is cur-5の51歳の女性は現在、長い懲役刑に服している rently serving a lengthy prison sentence/ in // 金曜 のだ/イランの悪名高きエビン刑務所で。 Iran's infamous Evin Prison.// After Friday's 日の (受賞の) 発表を受けて/フランスのエマニュ announcement,/ French president Emmanuel エル・マクロン大統領はモハマディ氏に対する賛 Macron lauded Mohammadi/ for her courage 辞を述べた/イラン当局に敢然と立ち向かう彼女 in standing up to the Iranian authorities.// 0 10 の勇気をたたえて。 // anibivong zodillatur

（2）の問題なんですが、なぜX軸方向に1,Y軸方向に-2動かせばいいのに、解答ではXに-1,Yに+2をしているんですか？

■練習 (1) 2次関数y=x²-8x-13のグラフをどのように平行移動すると,2次関数 ② 76 y=x2+4x+3のグラフに重なるか。 (2) x 軸方向に -1,y 軸方向に2だけ平行移動すると,放物線y=x2+3x+4に移 物線の方程式を求めよ。

空欄の所と間違えているところ教えて欲しいです🙇‍♀️🙏

6 分詞 (LESSON 14-15) 評価問題 氏名 ()から適切な語句を選びなさい。 ( 3点×4=12点) (1) This is a picture of a bird (drink/drinking/drunk) water from a pond. (2) We were (surprise/ surprised/ surprising) at her colorful dress. (3) The old man sat on the sofa with his legs (cross/crossing/ crossed). (4) My sister had her hair (cut/cutting/ to cut) by my mother. [ ] の動詞を適切な形にして、英文を完成させなさい。 to music. (1) Mike reads a book, listening (2) They left the gate Closiny all day long. (3) The picture (4) The boys kept Painted by Emma is very beautiful. Playing the computer game for hours. 13 ( )の語句を並べかえて、 英文を完成させなさい。 ただし、 下線部の動詞は適切な 形の分詞にすること ( 4点×5=20点) (1) (someone / in / there / of / is / front / wait) the door. There is someone wailing in front of (2) (got/cell phone/I/repair/my) yesterday. ( 4点×4=16点) [listen ] [close] [paint] [play] I got refailed my cell phone (3) We (the shop/ be baked / we / apple pies / at ). We (4) (a new restaurant/found/drive/he/ the car,) near his home. Priving the cat he found a new bestrant the door. /100 yesterday. near his home. (5) Ann watched (her cheeks/run/the movie / tears/down/ with). Ann watched the horie running dan with her checks teats ④4 次の各文の誤りを訂正して、全文を書きなさい。 (1) その眠っている赤ちゃんは私の息子です。 The baby sleeping is my son. The sleeping baby is my soul (2) 先生は彼の生徒たちに囲まれて座っていました。 The teacher sat surrounding by his students. the surrounding teacher sat by his students (3) お父さんに叱られたので、その女の子は泣き始めた。 Scolding by her father, the girl began to cry. Scolding by her father the girl began to ch (4) 彼女は車をそのホテルに駐車したままにしておきました。 She left her car park at the hotel. 5 次の日本語の意味に合う英文を作りなさい。 (1) 彼女は皿を洗うのに忙しかった。 (6点×4=24点) she was busy washing the dishes (I で始めて) I heard my brother singing the song (his で始めて (2) 弟がその歌を歌っているのが聞こえました。 (3) 彼のスピーチは退屈でした。 His speech was boring ( 6点×3=18点) 6 あなたが何かをしに行って, そのとき感じたことなどを3~4つの英文で書きなさい。 (5点) 会話の最後に入る気持ちを自由に考えて書きなさい。 A: The university entrance exam is coming up soon. B: I'm getting nervous. I don't know if I can pass or not. A: (5