画像下線部のカンマがついている理由がわかりません。

次の英文の下線部を訳しなさい It was at lunch on a cold Sunday in late January that we first heard the noise. It sounded like a tapping; slightly metallic Reluctant to leave the table, at first we speculated on the possibilities. But when the tapping became persistent, or rather insistent, we went to investigate. And so we came upon the blackbird, pecking at the window. (法政大)

英語の並べ替え問題です。 解説と解答お願いします。

(5) シドニー大学の研究者たちは、1匹のハコクラゲが60人もの人間を死なせるほど、いかにて 毒が致命的であるのかを調査してきた。 Researchers at the University of Sydney have 26 deadly that one box jellyfish can kill as many as 60 people 25 27 1 is 2 the ③ investigating 4 s0 5 venom 6 how 7 been

アから順番に12131であってますか？ わかる方教えてください！！ お願いします！

Earth has two sets of poles: the geographic poles and the magnetic poles. The geographic poles are located at the northemmost and southernmost ends of the earth. The location of the magnetic poles, on the other hand, are ( ア ) moving, This fact has several implications for navigation and transportation. Shifts in the position of the North Magnetic Pole are nothing new. Since 1831, scientists have been tracking its location. The movements are caused by changes in the flow of swirling molten iron in the earth's core which affect how the earth's magnetic field behaves. What is surprising to scientists is the speed at which the pole has been moving in recent years. For most of the 20th century, magnetic north was located around the northern parts of Canada. It drifted around, moving slowly north at an ( イ ) speed of approximately 10 kilometers per year. In recent decades, that rate has increased significantly to about 55 kilometers per year. The North Magnetic Pole is now moving away from Canada toward eastem Russia. While scientists can't fully explain how changes in the carth's molten core are affecting the pole's movement, they can map the earth's magnetic field. Doing so allows them to ( ウ) hé rate of change over time. This, in turn, provides information on how the magnetic field may shift in the future. Information on changes to the earth's magnetic field is used to produce the World Magnetic Model (WMM). This model is used as the basis for all fornms of modern navigation, from how ships move at sea to mapping software in smartphones. ( エ) in the model, caused by shifts in the real location of the North Magnetic Pole, can seriously impact almost all foms of modern transportation. The model is updated every five years, but in 2018, during routine checks of the 2015- 2020 model cycle, scientists noticed a problem. Because of the rapidly shifting pole, the WMM was close to being outside the acceptable limits for navigational errors. This forced the release of an updated version of the model、 It was revised ( オ ) in 2020, and the current version is expected to last until 2024, As well as keeping track of the WMM's accuracy, scientists continue investigating why the magnetic field is changing so dramatically. This essential work will ensure a safe journey for everyone navigating their way through the world.

ア順番に12131であってますか？ わかる方教えてください！！！！ お願いします！

For most of the 20th century, magnetic north was located around the northern parts of molten iron in the earth's core which affect how the earth's magnetic field behaves. What is surprising to scientists is the speed at which the pole has been moving in recent years. magnetic poles, on the other hand, are ( ア ) moving. This fact has several implications poles are located at the northernmost and southernmost ends of the earth. The location of the Shifts in the position of the North Magnetic Pole are nothing new. Since 1831, scientists Earth has two sets of poles: the geographic poles and the magnetic poles. The geographic have been tracking its location. The movements are caused by changes in the flow of swirling for navigation and transportation. Canada. It drified around, moving slowiy north at an ( イ ) speed of approximately 10 MIometers per year. In recent decades. that rate has increased significantly to about 3 KIIometers per year. The North Magnetic Pole is nowmoving away from Canada toward eastern Russia. While scientists can't fully explain how changes in the earth's molten core are affecting the pole's movement, they can map the earth's magnetic field. Doing so allows them to (ウ ) the rate of change over time. This, in turn, provides information on how the magnetic field may shift in the future. Information on changes to the earth's magnetic field is used to produce the World Magnetic Model (WMM). This model is used as the basis for all forms of modern navigation, from how ships move at sea to mapping software in smartphones. ( エ ) inthe model, caused by shits in the real location of the North Magnetic Pole, can seriously impact almost all forms of moderntransportation. The model is updated every five years, but in 2018, during routine checks of the 2015- 2020 model cycle, scientists noticed a problem. Because of the rapidly shifting pole, the WMM was close to being outside the acceptable limits for navigational errors. This forced the release of an updated version of the model. was revised ( オ ) in2020, and the current version is expected to last until 2024. As well as keeping track of the WMM's accuracy, scientists continue investigating why the magnetic ficld is changing so dramatically. This essential work will ensure a safe journey for everyone navigating their way through the world.

アから順番に12131であってますか？ わかる方教えてください！！ お願いします！

例3.次の英文は 「磁極の移動」について述べたものです。(ア) ~ (オ) に入れ る最も適当なものを選択肢から選びなさい。 Earth has two sets of poles: the geographic poles and the magnetic poles. The geographic poles are located at the northernmost and southernmost ends of the earth. The location of the magnetic poles, on the other hand, are ( ア ) moving. This fact has several implications for navigation and transportation. Shifts in the position of the North Magnetic Pole are nothing new. Since 1831, scientists have been tracking its location. The movements are caused by changes in the flow of swirling molten iron in the earth's core which affect how the earth's magnetic field behaves. What is surprising to scientists is the speed at which the pole has been moving in recent years. For most of the 20th century, magnetic north was located around the northern parts of Canada. It drifted around, moving slowly north at an ( イ) speed of approximately 10 kilometers per year. In recent decades, that rate has increased significantly to about 55 kilometers per year, The North Maggnetic Pole is now moving away from Canada toward eastern Russia. While scientists can't fully explain how changes in the earth's molten core are affecting the pole's movement, they can map the earth's magnetic field. Doing so allows them to ( ウ ) the rate of change over time. This, in turn, provides information on how the magnetic field may shift in the future. Information on changes to the earth's magnetic field is used to produce the World Magnetic Model (WMM). This model is used as the basis for all forms of modern navigation, from how ships move at sea to mapping software in smartphones. ( エ ) inthe model、 caused by shifts in the real location of the North Magnetic Pole, can seriously impact almost all foms of modern transportation. The model is updated every five years, but in 2018, during routine checks of the 2015- 2020 model cycle, scientists noticed a problem, Because of the rapidly shifting pole, the WMIM was close to being outside the acceptable limits for navigational errors. This forced the release of an updated version of the model, It was revised (オ ) in2020, and the current version is expected to last until 2024, As well as kecping track of the WMM's accuracy, scientists continue investigating why the magnetic ficld is changing so dramatically, This essential work will ensure a safe joumey for everyone navigating their way through the world.

和訳お願いしたいです

greaty respected Greek philosopher Aristotle (384-322 BC), who claimed that heavy Objects naturally fall faster than light obiects. This hypothesis was considered to be true nearly 2000 years-mainly because nearly everyone who knew of Aristotle's Conclusions had such great respect for him as a thinker* that they simply assumed he Couldn t be wrong. Also, in Aristotle's time. air resistance was not recognized as an Iuence on how quickly an obiect falls We've all seen that stones fall faster than leaves Inuttering in the air. Without investigating further, we can easily accept false ideas. Ganleo very carefully examined 。 Aristotle's hypothesis. Then he did something that -Q 10 caught on and changed science forever. He experimented. Galileo showed the falseness of Aristotle's claim with a single experiment ー dropping heavy and light objects from the Leaning Tower of Pisa. Legend tells us that the objects fell at equal speeds. (3) In the SCientific spirit, one experiment that can be reproduced outweighs any authority, regardless of reputation or the number of advocates* CD 58

Tactics for TOIEC, listening and reading testの P.26-27のB:Minitestの解答教えてほしいです😖 よろしくお願いします

ETS, Listening. Learning. Leading. Content is authorized by ETS and contains official TOEIC® test items Tactics for TOEIC Listening and Reading Test Grant Trew OXFORD 1|日こ

この英文の()に入る言葉が全然分かりません。 分かるところだけでも大丈夫なので説明してほしいです！

|1| The conversation begins with a British professor talking to a Japanese professor about a lesson he had conducted with his Japanese students. He explains how one of his students ( ① ) him by referring to one of the colors of traffic lights as blue 及する 指角する ( 2 ) of green. The Japanese professor points out that in the Japanese language some objects that are usually thought of as green in many languages are ((3 ) using a Japanese word for blue. The British professor then describes similar ( ④ ) in other languages and cultures, such as that of the Berinmo in Papua New Guinea. They also discuss how Japanese and other languages also have ( ⑤ ) words for light blue and blue. 特称もべろ 2| This leads to a discussion about whether Japanese people are( ⑥ ) different things when they look at objects, or whether they are just ( ⑦ ) different terms to describe them. The British professor then brings up a study that investigated how bilingual speakers of Greek and English ( ③ ) different shades of blue. He notes that the conclusion of the study was that those people who spent more time in the UK were ( 9 ) likely to describe the shades of light blue and blue as very different from each other. 3 The Japanese professor continues the conversation by bringing up a second study that further examines the idea that language can( 10 ) the way we think. This study involved Japanese and English speakers and found that the Japanese speakers judged shades of light blue and blue to be further apart. Both professors conclude the discussion by noting the ( ① ) in interpreting the results of these studies, with the Japanese professor observing that language could be influencing thought or that other ( 2 ) factors could be at work. (D) separate (B) cultural (F) effect (A) assessed (C) characteristics (G) society (H) in contrast (E) less (K) disagreeing (O) surprised (S) designed (W) seeing (L) more (1) using (J) instead (N) mistakes (P) dificulty (M) felt (T) critical (X) increasing (Q) need (R) affect (U) reinforce (V) referred )6(W) へ の( )の( C ) ⑤ ( の( 9

青学の赤本で、配点が書いてないので分からないのですが、この文だとどのくらいの割合の取れるか採点して頂きたいです。また改善点などあれば教えてください。

Rarely, baibmlo asil aot bsotlie: ofh batsvsan dvad oT3 19vi liM adi1o dgnol lni ods bexlsw avad oT © 問題IV 次の設問について, 50 語程度の英文を書きなさい。解答用紙(その3)を 使用。 Mostof the ime. because e traveled alone and nie V li od gnols alsw a'booW noaived asvw gaol woll St Choose a foreign city that you would like to visit anywhere in the world, and explain why you would like to visit that city. nol aslim OS 22 In Leviso ynbl afie travel? nol 2olim OSSO Changing his Avoiding pftigadigahuoi nsohlA abooW noeivs.J bib e9d W 81 sbu2 dol ① Being bord

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... 続きを読む

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.