「教科書のこの部分の要点を日本語で書け」 なんて書けばいいでしょうか😵‍💫😵‍💫

10-2 Expressing the Past: Necessity, Advisability, Expectation PRESENT:(a) Julia has to get a visa. (b) Julia has got to get a visa. (c) Julia must get a visa. Past necessity: had to In (d): had to needed to: Julia needed to get a visa. There is no other past form for must (when it rmeans neceasity) or have got to. PAST: (d) Julia had to get a visa. PRESENT:(e) I should study for the test. I want to Past advisability: pass it. (f) lought to study for the test. (g) T had better study for the test. should have ought to have + past participle In the past, should is more common than ought to. The past form of had better (had better have) is almost never used. PAST: Ifailed the test. (h) Ishould have studied for it. (i) lought to have studied for it. (i) I shouldn't have gone to the movies the night before. The meaning in (h) and (i): Studying was a good idea, but 1 didn't do it. I made a mistake. The meaning in (j): It was a bad idea to go to the movies. I made a mistake. Usual pronunciation of should have: “should-ev" or “should-e." lao was/were supposed to: unfulfilled expectation or obligation in the past PRESENT:(k) We are supposed to leave now. PAST: (1) We were supposed toleave last week. PRESENT:(m)The mail should be here. Should have + past participle: past expectation The speaker expected something to happen%; it may or may not have occurred, as in (n).. PAST: (n) The mail should have been here by now.

間違えが10個あります。 教えてください。

On July, a Japanese friend named Toshi and I decided to climb Kitadake, who is Japan's second highest mountain. Knowing this wouldn't be easy 1I started training. I went jogging and swimming regularly to trying and prepare and was feeling fit and ready at the end of July. At the beginning of August, the number of Corona cases was increasing so unfortunately we had to change our plans. Toshi doesn't want to catch the bus from Kofu to the Suothern Alps because of the risk of Corona infection, so we stayed in Shizuoka prefecture. Yanbushi was a mountain, 2014 meters high. It is not far from Umegashima, which is famous for it's hot springs. Instead of Kitadake, we climbed Yanbushi. In August 10, we woke up early and drove to the starting point. It was the day after a typhoon had passed and a beautifull, clear morning in Shizuoka city. However when we arrived, it was very cloudy and it was raining lightly. After a three and a half hour climb we arrived at the summit. It rained most of the way but it wasn't so bad under the trees and actually kept us cool. It was a challenging and rewarding experience. Ithink exploring nature is a fun, healthy and interesting way to spent your free time. T have included a photo of my climb.

緊急です、数学のプリントの1枚目の3だけでも解いてもらえると嬉しいです！

Aa直し用 929提出 庄田 5. 応用数学a 前期期末試験 (No.1) 2021.8. No.3 裏の注意をよく読んでから、 問題を解きなさい。 3n-i 1. 第n項が 1+2ni, lim ヲイー1 こlim ラー-2 >0H2Mi 900 tiI 27 2. 級数 の収束、発散を調べ、 収束する場合はその和を求めよ。 =0 HにECOS会+isin H-CoS+isin 3. 関数f(2) = 1 の0を中心とするテイラー展開と収束半径を求めよ。 2-2 6. 関 4. f(2)=は+1) 1 -について次のに答えよ。 (1) 0を中心とするローラン級数と、このローラン級数が収束する領域を求めよ。 この関数の孤立特異点とその種類を言え。

問題814、接続詞の問題です。解答は④のWhenなのですが、③のSinceが不正解である理由が分かりません。「春がきたので、多くの教授が戸外で授業を行う。」という和訳ではおかしいでしょうか。

) spring comes, many professors move their classes の which 2814.( outdoors. の Although ② However 19V9woH S)n9v3) 3 Since ④ When がタメな理的は、hod 愛応 10mn him put yourself in his place. M9I0n1oL_200gOn

黄色いマーカーの問題でどうしてなるのか知りたいです 教えてくれるとありがたいです(;_;)

Tm not sure if Tll ( ) it to the meeting in time. 2 闘1、 0 access Oacute 落統 保製はひとれ。 Oannual O aisle 年回の 23. Sure nを確信 0 Come 2 have make の see The subway is under ( ). but it's easy to get to the hotel by bus. 3 通路 4. 0 constitution construction consultation @ consumption T hope(that the video clip will be( interest to you. 4 (0 at 2 in of on の

67の答えがCなのですがおかしくないですか？恐らくCEOの事を書いているのだと思いますがCEOと社長presidentは別の役職で同じではないと思ったのですが

65-67 refer to the following conversation. W: Richard, we were deeply impressed with your presentation this morning. You concentrated on the benefits the customers 65. What did the man do this morning? OEIC (A) He had a talk with an executivetsTENING will get from our new products. That was awesome. The sales manager wants you to give a presentation on the same topic to the board of directors next week. (B) He gave a talk. (C) He made a presentation to the board of directors. (D) He put together handouts. 66. What does the woman suggest? I'm glad you liked it. I'l try my best to please the board of directors. Maybe l could use some technology to supplement my presentation. Don't you think using a video allows the audience to understandit (A) Preparing more informative materials (B) Using a video (C) Getting advice from the sales manager (D) Choosing a new topic M: ,Com, /。 better? W: That's a good idea. You should prepare more extensive handouts as well. I will be free this afternoon, so l can help you put them together. M: I'd appreciate it. Let's make it our top priority to ensure that our executives are satisfied. Even the CEO will be there. 67. What does the man say about next week's presentation? (A) It will take place in the afternoon. (B) It will concentrate on the benefits of video presentations. (C) The president will see it. (D) The sales manager will help them prepare for it. 65B 66A 6

解き方が分かりません

10点×6 1 次の数量を表す式をつくりなさい。 (1) 1個a円の消しゴム3個と1本6円のボールペンを2本買ったときの代 1 金 (2) 枚の紙を12人の子どもにy枚ずつ配ったときの,残った紙の枚数 (3) 縦a cm, 横b cm の長方形の面積 (4) mでわると商が7で余りがnになる自然数 (5) 時速5km でェ時間歩いたときの進んだ道のり (「km」の単位で表す) (6) km の道のりを分速 50m で進むときにかかる時間(「分」の単位で表す) 2右の図のように,長さ 20cmのテープ -20cm 2 10点×2 を左から順にのりしろを5cm としてつ ないでいく。このとき,次の問いに答え なさい。 (1) テープを4枚つないだとき、全体の長さは何 cm ですか。 5cm (2) テープをn枚つないだとき,全体の長さは何 cm ですか。 3 次の数量の関係を等式や不等式で表しなさい。 3 10点×2 a個のりんごを6人の子どもに2個ずつ配ったら,残りは4個だった。 (2) ある数ェを5倍した数は,ある数yに7を加えた数より大きい。

量子力学・ハイゼンベルクの交換相互作用についての問題です。 参考書を参考に(あ)〜(え)まで解いてみたのですが、考え方はあっていますか？ また、(お)以降の解説をお願いします。ブロッホの定理やフーリエ変換はどのように効いてくるのでしょうか？

III. 以下の文章のあ き の枠内に当てはまる数式や記号を答えよ。 ヘ =1として,スピン角運動量1/2をもつ三つのスピンが,互いに相互作用している系を考え る。スピン演算子を$, S,, $, とすると,系のハミルトニアンは次のように与えられる。 自=-J(S, S+ S,. S。+ $。. S.), J>0. ここでも番目(;= 1,2,3) のスピンのz,9, z 方向成分をそれぞれ好,S, S とする。スピン演算 子の間には (S, SY] = iS}, [SF, SY] = 0などの交換関係が成り立つ、自) = E\d) を満たす。 固有エネルギーEとエネルギー固有状態|)を求めたい。 全スピン角運動量 Shot = $, + $2+S。を使うとハミルトニアンは次のように書き直すことが できる。 自= - + JC, 定数C= あ 'tot このことから基底状態のエネルギー固有値は 時の固有値は S= +1/2, -1/2 のニつであり,これらに相当する1スピン状態をそれぞれ↑。 ↓と記すと,3スピン状態は,|S{ S S3) = |M1),| t)などのように表すことができる。独 立な3スピン状態は全部で 具体的にエネルギー固有状態をあらわしてみよう。 まず基底状態のうちで Sto = St+ Sz + Sg が最大の状態は |S S; Sg) ちに書き下すことができる。 つぎにエネルギー固有状態のうちで Sie = 1/2 のものを求めたい,ハミルトニアンと交換可 能な演算子はハミルトニアンと同時固有状態をもつことを利用する.このような演算子の一つ にスピンをRIS; S; S) = |S; S; S;)のように巡回置換する演算子良がある。-iとなるこ とと,周期系におけるブロッホの定理やフーリエ変換を思い出すと,Rと St。と自の同時固有 状態は適切な定数A(複素数も含む)を用いて い である。 う 種類あり,規格直交基底をなす。にれらの線形結合の形で え のように直 三 る(「4)+A|)+ ^°| +t) V3 と表せることが分かる。Aの取り得る値をすべて列挙すると 底状態となるのは A- か 以上の結果からすでに二つ基底状態が得られた。残りの基底状態を列挙すると, お となる.このうちで,基 の場合である。 き と なる。

多様体の接空間に関する基底定理の証明です。g(q)=∫〜と定義した関数を微積分学の基本定理を用いながら変形してg(q)=g(0)+∑gᵢuⁱと導出するのですが、これがうまくいきません。 自分は、g(q)の式をまず両辺tで微分して、次に両辺uⁱで積分して、最後に両辺tで積分... Read More

12. Theorem.If{ = (x', , x") is a coordinate system in M at p, then its coordinate vectors d, lp, …… 0,l, forma basis for the tangent space T,(M); and D= E(x) 。 i=1 for all ve T(M). Proof. By the preceding remarks we can work solely on the coordinate neighborhood of G. Since u(c) = Othere is no loss of generality in assuming ど(p) = 0eR". Shrinking W if necessary gives E(W) = {qe R":|q| < } for some 8. Ifg is a smooth function on E(W) then for each 1 <isndefine og (tq) dt du g(9) = for all qe {(W). It follows using the fundamental theorem of calculus that g= g(0) + E&,u' on (W). Thus if fe &(M), setting g = f。' yields f= f(P) + Ex on U. Applying d/ax' gives f(p) = (f /0x)(P). Thus applying the tangent vector e to the formula gives (f) = 0+ E(x'(p) + E Ap)u(x) = E(Px). ず ax Since this holds for all f e &(M), the tangent vectors v and Z Ux') d,l, are equal. It remains to show that the coordinate vectors are linearly independent. But if ) a, o.l, = 0, then application to x' yields dxi 0=24 (P) = 2q d」= 4. In particular the (vector space) dimension of T,(M) is the same as the dimension of M.

問題の解き方や、答えが分からないです。また、問題を解くために高校数学や大学数学のどの単元の知識が使われているのかも合わせて教えて頂きたいです。よろしくお願いします。

問(i)~(vi) に答えよ。 解答は解答用紙の所定欄に日本語で記すこと。 導出過程も簡潔に記す こと。 Let the function f(n) be defined as S(n) = cos? where n and 入 are positive integers (greater than 0). (i) Assuming n>1000 and 42 < 76, determine f(n). (i) Assuming is a prime number, determine the smallest n such that 『(n) = cos? %D