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数学 大学生・専門学校生・社会人

問題としてはこのURLのやつでexercise2.2.9の問題です。 2.2.9. Define T : ℓ^2(Zn ) → ℓ^2(Zn ) by (T(z))(n) =z(n + 1) − z(n). Find all eigenvalues of T.... 続きを読む

16:22マ l 全 の Exerc: 164/520 matrices, convolution operators, and Fourier r operators. 2.2.9. Define T:l'(Zn) - → e°(ZN) by ニ Find all eigenvalues of T. 2.2.10. Let T(m):e'(Z4) → '(Z) be the Fourier multipliei (mz)' where m = (1,0, i, -2) defined by T (m)(2) = i. Find be l(Z4) such that T(m) is the convolutior Tb (defined by Th(Z) = b*z). ii. Find the matrix that represents T(m) with resp standard basis. 2.2.11. i. Suppose Ti, T2:l(ZN) → e(ZN) are tra invariant linear transformations. Prove that th sition T, o T, is translation invariant. ii. Suppose A and B are circulant NxN matric directly (i.e., just using the definition of a matrix, not using Theorem 2.19) that AB is Show that this result and Theorem 2.19 imp Hint: Write out the (m + 1,n+1) entry of the definition of matrix multiplication; compare hint to Exercise 2.2.12 (i). iii. Suppose b,, bz e l'(Zn). Prove that the cor Tb, o Tb, of the convolution operators Tb, and convolution operator T, with b = 2 bz * b.. E Exercise 2.2.6. iv. Suppose m,, mz € l"(Z). Prove that the cor T(m2) ° T(m) and T(m) is the Fourier multiplier operator T) m(n) = m2(n)m」(n) for all n. v. Suppose Ti, T2:l"(Zw) → e'(Zn) are linear tra tions. Prove that if Ti is represented bya matri respect to the Fourier basis F (i.e., [T; (z)]F =A Tz is represented by a matrix Az with respect t the composition T20T, is represented by the ma with respect to F. Deduce part i again. Remark:ByTheerem 2.19, we have just proved of the Fourier multiplier operat Aresearchgate.net - 非公開

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理科 中学生

(6)と(7)を教えて頂きたいです(><)

探究問題 大の 体の物質が水に溶けるようすを調べるため。 美験を行った。図は,水100gに溶ける硝酸カリ ゥムと塩化ナトリウムの質量とそのときの水の温度 を表した溶解度曲線である。あとの問いに答えなさ ただし,実験中の水の蒸発はなく, 硝酸カリウ ムと塩化ナトリウムの溶解度は,ほかの物質が混さざ っていても互いに影響を及ほさないものとする。 「実験1] 2つのビーカーX, Yを用意し,それぞ れに水100gを入れ,2つとも50Oになるまで加熱した。加熱をやめ,その温度を保った まま,ビーカーXには硝酸カリウムを40g,ビーカーYには塩化ナトリウムを30。 ガラス棒でかき混ぜてすべて溶かした 。 (実験2] 50℃のビーカーXの水溶液の半分を新しく用意したビーカーAにううしだ。さら (octll にビーカーAの水溶液の温度を10Oになるまで冷却した。 (1)一定量の水に物質を溶かしていき, 物質がそれ以上溶けること のできなくなった水溶液のことを何というか。 (2) 実験1で, ビーカーXとYの水溶液の質量パーセント濃度はそ れぞれ何%か。小数第1位を四捨五入して, 整数で答えなさい。 (3) 実験1のビーカーXの水溶液にさらに硝酸カリウムを溶かした 水 200 100 150 る 100 硝酸カリウム 50 塩化ナトリウム| coog9 yうOf 80 0 20 40 60 温度(℃) 5'c 7 as 州ム[の湯ける 30% |707 れいきゃく 70 x(292 Y 23% とき,すべて溶けて水溶液の質量パーセント濃度がもっとも高く なるのは,硝酸カリウムをあと約何g溶かしたときか。次のア~ エから選び,記号で答えなさい。 ア 25g (4)実験2で,ビーカーAの水溶液の濃さは, 水溶液を半分にする 前のビーカーXの水溶液の濃さと比べてどのようになったか。 なわらな。 イ 35g ウ 45g エ 55g (5) 実験2で,10℃になるまで冷却したビーカーAの中の水溶液は 約何gか。次のア~エから選び, 記号で答えなさい。 ウ 60g 259 水50g り 20g 全体 70g ア 40g イ 50g エ 70g I 6)(5)で得たビーカーAの水溶液と同じ質量パーセント濃度の水溶 液を150gつくるには, 硝酸カリウかが何g必要か。 X(7) 新しくビーカーをもう1つ用意し,硝酸カリウムと塩化ナトリ, ウムをともに72gずつ入れた。これら2つの物質を完全に溶かす のに、50の水は少なくと、も何g必要か。次のア~オから選び、 記号で答えなさい。 too)ド 20}溶ける (10-(0) ア 50g イ 100g ウ 150g え ー 北 I 200g オ 250g S° 水8gに溶ける物質の質量8

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英語 高校生

答え合わせがしたいので教えてください

「I|次の文を読んで、あとの問いに答えなさい。( wのついた語は文末に注があります。 ns Sitting in the consultation room of a charming cosmetic surgery clinic in Washmgo. D.C., Hudson Young removed his mask under the satisfied gaze of his doctor. Like a grownns number of Americans, Young decided the right time to undergo plastic surgery was middle of a coronavirus pandemic, He knew he would have time to recover in the privacy ot his own home. The main reason, however, was that Young suddenly found himself face to face with his own image while participating in an increasing number of videophone and web A 「Its something new when you have to stare at your face for a couple of hours a day and there's only so much you can do with good lighting and good angles," Young said. The 52-year-old real estate agent had allready been a fan of cosmetic surgery. He had face lift, eyelid surgery and laser resurfacing for the first time in October. "When you see yourself on Zoom, you are shocked," he explained, as Dr. Michael Somenek examined his w barely visible scars. Young is far from the only one who has found himself disappointed with the reflection he has seen in the screen over the past year. Virtual consultations for cosmetic procedures have risen 64% in the United States since the beginning of the COVID-19 pandemic, according to the American Society of Plastic Surgeons. “We have seen an increase in the number of surgical cosmetic procedures that are directly related to Zoom," said Somenek, who has seen a 50% to 60% increase in customers. “I think the pandemic B has given everyone time to take care of those things that we've been putting off until later," explained Ana Caceres, who was able to work from home after C a plastic surgery operation she had wanted for a long time. She recovered at. her parents' house outside Washington after a December cosmetic surgery that helped her D deal with a source of insecurity she had had since adolescence. "I didn't have to days off, because I was still able to work from my bed with my lap-top," the 25-year-old said. “When life is going on and you have places to be, it's s0 easy to put things off," Caceres said, showing off a dress she says she now has the confidence to wear. And she has scheduled more cosmetic surgery. Her surgeon, Dr. Catherine Hannan, says consultations at her clinic in the IIS comit1 E have nearly doubled since the beginning of the pandemic. "Our patients have more lines because the last vear has been so hard. A face or boay change can have a psychological

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英語 高校生

教えてほしいです!!お願いします!!

問題は【1】~【4】まである。答えは各問題の指示に従って別紙の解答用紙に書きなさい。 【1】次の英文を読んで設問に答えなさい。 Headaches are a big problem. Each year, millions of people suffer from severe headaches that affect their enjoyment of life, (1) not to mention their productivity at work. estimate, headaches cost individuals and businesses more than (2) $50 billion each year! (3) This is one of the reasons research into headaches has become a worldwide effort. Although he did not know much about how headaches work, Hippocrates was the first doctor to find a way to treat them. By 400 BC, Hippocrates had discovered that the *bark from willow trees was useful in treating pain. He made a white powder from the tree's bark and gave it to his patients. Hippocrates did not know it, but he was actually prescribing a natural chemical in willow bark called salicin. Whena person eats salicin, the chemical is changed inside his or her body into (4) salicylic acid. It turns out that salicylic acid is good for stopping pain, including headache pain, but it is bad for a person's stomach. In the 1800s, a chemist in Germany slightly changed easier for people to take. commonly known as aspirin. Aspirin was used throughout most of the 1900s to treat headaches, but doctors had little idea about what really caused headaches. When doctors can *diagnose the cause of a disease, they can find better ways to treat it. Therefore, as medical technology developed, doctors began to use it to learn more about the human brain and about headaches. In fact, according to one m to make it This new form of the chemical was called acetylsalicylic acid, now acid's Now doctors classify headaches ( A ) two general types: primary and secondary. A primary headache is a condition ( B) as only the headache itself. one caused by another physiological condition, such as an *infection or a *tumor. For primary headaches, doctors have determined three possible causes. headache is caused by stress. characteristically felt on both sides of the head as a dull, steady pain. Another kind of primary headache is the *migraine headache. Exactly what causes these headaches is not well understood, but many experts believe it could be abnormal brain activity causing changes in the brain's chemistry and blood flow. For many people, migraines are caused by certain (5) stimuli, such as poor sleep or particular foods or smells. A sufferer usually feels intense pain on one side of the head and becomes sensitive to light and noise. If the migraine is severe, the sufferer may *vomit repeatedly. The third kind of primary headache is known as the cluster headache. Cluster headaches typically occur around the same time each day for weeks or months at a time. The person ( C)from this kind of headache usually feels pain on one side of her or his head, and the pain is centered around one of the eyes. Doctors do not know much (6) at present about cluster headaches, but they seem to be more common among men and could be related to alcohol or other things that affect a person's blood flow. Using computers and more advanced medical equipment, doctors continue to learn more about what happens in the brain before and during headaches. Especially in the case of migraines, some doctors believe they have found the part of the brain that sets off the reaction for severe attacks. With these insights into brain processes, doctors hope new ways will be discovered to stop headaches before they begin. On the other hand, a secondary headache is One kind of primary Doctors usually call these tension headaches, and they are 注: bark 樹皮 diagnose ~を診断する、~を突き止める 感染症·伝染病 migraine (headache) 偏頭痛 infection tumor 腫場 vomit 食べたものを吐く (出典:READING FOR THE REAL WORLD 3rd edition, Compass Publishing より)

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