Cho hình chóp \(S. A B C\) có đáy \(A B C\) là tam giác đều cạnh \(a\) và \(S A=S B=S C=b(a>b \sqrt{2})\). Gọi \(G\) là trọng tâm \(\triangle A B C\). Xét mặt phẳng \((P)\) đi qua \(B\) vuông góc với \(S C\) tại điểm \(I\) nằm giữa \(S\) và \(C\). Diện tích thiết diện của hình chóp khi cắt bởi mặt phẳng \((P)\) là
\(S=\frac{a^{2} \sqrt{3 b^{2}-a^{2}}}{2 b}\).
\(S=\frac{a^{2} \sqrt{3 b^{2}-2 a b}}{4 b}\).
\(S=\frac{a^{2} \sqrt{3 b^{2}+a^{2}}}{2 b}\).
\(S=\frac{a^{2} \sqrt{3 b^{2}+a^{2}}}{4 b}\).
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Kẻ \(A I \perp S C \Rightarrow(A I B) \perp S C\). Thiết diện là tam giác \(A I B\)
Ta có \(A I=A C \sin A C S=a \sqrt{1-\cos ^{2} A C S}=a \sqrt{1-\left(\frac{a^{2}+b^{2}-b^{2}}{2 a b}\right)}=\frac{a}{2 b} \sqrt{4 b^{2}-2 a b}\)
Gọi \(J\) là trung điểm của \(A B\). \(\triangle A I B\) cân tại \(I\) suy ra \(I J \perp A B\)
\(I J=\sqrt{A I^{2}-A J^{2}}=\frac{a}{2 b} \sqrt{3 b^{2}-2 a b} \Rightarrow S=\frac{1}{2} A B. I J=\frac{a^{2} \sqrt{3 b^{2}-2 a b}}{4 b}\).
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Quang hợp ở cây xanh chỉ xảy ra vào ban ngày khi có ánh sáng, còn hô hấp ở thực vật diễn ra vào lúc nào?
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Read the following passage about lifelong learning and mark the letter A, B, C, or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
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It’s not just the uncertainty of travel that we all have to face. None of us knows what is going to happen, or what is currently going on outside our immediate knowledge, or the vast majority of what has happened in the past. Uncertainty has been called the “conscious awareness of ignorance,” and there is a lot we are ignorant about. We must navigate through life without complete information, and this fundamental uncertainty is an inescapable aspect of human existence.
We all have to live with this uncertainty and, as a statistician, it’s been my job to try to analyse data and assess some of the risks we face. (I)But some deal with uncertainty with more equanimity than others. (II) Psychological studies, as well as our own experience, reveal a wide variation in people’s responses, including those that are cognitive (how we think), emotional (how we feel), and behavioural (what we do). (III)For example, when faced with uncertainty, do you deny it or acknowledge it, does it put the wind up you or make you courageous, do you try to avoid it or approach it?(IV)
Of course, your response may depend on the context, just as an individual’s appetite for risk-taking can vary across different areas of their lives. I have known people who seemed to take huge physical risks, yet were very cautious with money. Numerous scales have been developed to measure how well people can deal with uncertainty, based on responses to statements ranging from “Unforeseen events upset me greatly” to “When it’s time to act, uncertainty paralyses me.” Those who score highly, and find it difficult to tolerate uncertainty, may also be at increased risk of clinically significant anxiety and depression.
Which of the following can be inferred from the passage?
Ai là tác giả của tác phẩm kịch Rô-mê-ô và Giu-li-ét?
Cho tam giác có độ dài ba cạnh lần lượt là \(1\), \(2\), \(\sqrt{5}\). Độ dài đường cao ứng với cạnh lớn nhất bằng
Choose the word that differs from the rest in the position of the main stress: parent, moment, packing, agree
Các nhà nước cổ đại ở Hy Lạp và La Mã ra đời vào khoảng
Read the following leaflet and mark the letter A, B, C, or D on your answer sheet to indicate the option that best fits each of the numbered blanks from 7 to 12.
Here are some ways to help reduce global warming. Which of these do you regularly do?
Don't use private cars. Your willingness to walk or cycle to nearby places can help reduce the emissions of carbon dioxide and also reduce your own carbon footprint. Use public transport. If travelling long distances, then use public transport rather than your car. However, if you carpool (travel together with a group of people in one car), then you are choosing to help ___(7)___ environment. If we travel with ___(8)___, we will use less petrol.
Make a decision to reduce, recycle, and reuse. Reduce waste by buying reusable products. Don't forget to recycle plastics, glass, and paper products. You may wish to reuse some of your old items to ___(9)___, too. Take unneeded ___(10)___ to a recycling centre.
Buy local goods. When you buy goods ___(11)___ from far-away places, it takes a lot of energy to ___(12)___ them to your area. This means that if you don't buy local food and products, then more emissions of carbon dioxide will happen during the transportation process.
(Adapted from English Discovery)
Cơ sở quan trọng để hình thành các tổ chức liên kết khu vực là gì?
Một quả bóng bầu dục có khoảng cách giữa 2 điểm xa nhất bằng 10 cm và cắt quả bóng bẳng mặt phẳng trung trực của đoạn thẳng đó thì được đường tròn có diện tích bằng \(16 \pi\left(\mathrm{~cm}^2\right)\). Thể tích của quả bóng bằng (Tính gần đúng đến hai chữ số thập phân, đơn vị lít)
GPS do quốc gia nào dưới đây xây dựng, vận hành và quản lí?
Read the following passage about the impact of tweeting on everybody and mark the letter A, B, C or D on your answer sheet to indicate the option that best fits each of the numbered blanks from 18 to 22
EVERYBODY’S TWEETING
Twitter (18) ________________ for a podcasting website, but then people realized that it offered them the power to connect with millions of people instantly. Suddenly, everyone had a voice, as long as it wasn’t longer than 140 characters. But what are we using it for, and just how is Twitter changing the way we do things?
Perhaps the greatest impact Twitter has had is on breaking news. Before Twitter, (19) _____________ before finally broadcasting it on the radio or TV. These days, anyone who happens to be in the right place at the right time with a Twitter account can post news the second it happens. For example, Janis Krums posted a photo and a tweet when he witnessed a US flight making an emergency landing in the Hudson River. He must never have imagined that he would break the story to the world.
Following Pop Idols
Young people have always loved to follow their pop idols, and Twitter has made it a whole lot easier. Before the Internet, teenagers used to join the fan clubs of their favorite bands and write letters to their heroes,
(20) _________________ to get a reply written by the club secretary. Today’s teenagers don’t need to wait. By following their idols on Twitter, they get all the news the minute it happens: their meals, activities, or even thoughts. And all the news comes directly from the bands themselves.
Creating Movements
Twitter allows people who think the same way to get together and (21) ______________. These problems may be cyberbullying, sexism, or racism. They can share information, organize campaigns, and put pressure on related departments. Twitter has given the man and woman on the street the power to make a difference.
Identifying the source of a piece of news
It’s good to get an idea of the background of a person who says or writes something. Are they an impartial expert or someone who wants to change your opinion to suit their own agenda? For example, this statement about a flu epidemic, “Patients can already spread the virus a day before they’ve even fallen sick themselves”, is more likely to come from a doctor than a politician. On the other hand, “We have to stop people who are carrying the virus from getting into the country” is more likely to come from a politician. (22) _____________, you’re better able to decide how much importance to give it and whether you can really trust what they say.
Ý nào dưới đây là nói về thuế gián thu?
Từ Hán Việt "quý nhân" có nghĩa là
Mark the letter A, B, C, or D on your answer sheet to indicate the word(s) CLOSEST in meaning to the underlined bold word(s) in each of the following questions.
The injured athlete was told that the effect of the anaesthetic wore off, he might feel a little pain.
Quá trình nguyên phân xảy ra ở loại tế bào nào sau đây?
Cho mệnh đề chứa biến P(x): "x+10≥x2" với x là số tự nhiên. Mệnh đề nào sau đây sai?
Đặc trưng nào khiến các làng xóm người Việt trở thành nơi xuất phát của các cuộc đấu tranh giành độc lập dưới thời kì Bắc thuộc?
Cực đại của hàm số \(y=\sqrt{8+2 x-x^{2}}\) bằng bao nhiêu?
