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English Junior High

3.4枚目が問題文、5枚目が答え、1.2枚目は問題を解くときに必要な文です。 なぜこの答えになるのかがわからないので教えてください。 解くのは大変だと思うので、一問だけでも大丈夫です。

2 次は, 高校1年生の Yusuke が書いた英文です。 これを読んで、 問1~間6に答えなさい。*印 のついている語句には、本文のあとに 〔注〕があります。(34点) My father loves *dinosaurs and *fossils. He (he/them/in/collects/is/that/interested /so) dinosaur toys, small fossils and books about dinosaurs. I heard he tried to find fossils along the river with my grandparents when he was young. When I was younger, my family took me to the science museum every year. My father loved looking at the dinosaur fossils there, and he always explained them to me. So, I got interested in dinosaurs and fossils, too. My father has a restaurant near our house, and he displays some dinosaur teeth fossils in the restaurant. One day, he introduced one of his customers to me. The man, Mr. Shirai, also loved dinosaurs and fossils, and often visited museums all around the world, such as in America, Canada and China. He realized that my father was interested in the same things because of the fossils in the restaurant. They became good friends. One day in September, Mr. Shirai came to my father's restaurant and showed me a fossil. It was a beautiful fish fossil in a brown stone plate. I was surprised to see it, Mr. Shirai A me a lot about the fossil. He traveled to Germany to look for fossils, and he found many fossils there such as fish, animal bones and leaves. The area is very famous for "archaeopteryx fossils. I once saw a picture of the archaeopteryx fossil in a book, so I wanted to go to see the fossil in -4-

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Mathematics Undergraduate

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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English Senior High

2行目でorが出てきたんですが、これはandではダメなんですか? なぜかも教えてくれると嬉しいです

44 友達同士が音楽について話をしています。 ① She thinks folk songs are boring. ② She prefers country music to folk songs. 3 She listens to the same kind of music as the man. ④ She does not like the music the man listens to. M: What kind of music do you like? W: I usually listen to country music or folk songs. M: How can you stand that boring stuff? W: The music you like gives me a headache! 「かまつ、気にかける」! 解答 設問と選択肢の訳 「料理する」 「雨の中を散歩に連 れていく」 女性は何をほのめかしていますか。 ① 彼女はフォークソングは退屈だと思っている。 ② 彼女はフォークソングよりカントリー・ミュージックの方が好き? ③ 彼女は、男性と同じ種類の音楽を聴く。 ④ 彼女は、男性が聴く音楽が好きではない。 全訳 男性: どんな音楽が好きなの? 女性: たいてい カントリー・ミュージックかフォーク・ソングを聴くわ。 男性: 何でそんな退屈なものを我慢できるんだろうね? Destion What does the woman suggest? 女性 あなたが好きな音楽を聴くと私は頭痛がするわ。 Point 女性の The music you like gives me a headache! という発言より、丸 が聴く音楽がうるさいので聴きたくないことがわかる。 リスト country music 「カントリー・ミュー ジック」 · folk song that boring stuff give A 「フォーク・ソング」 stand 「あんな退屈なもの」 「Aに 解答 「・・・を我慢する」

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