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Câu hỏi:

Read the following passage about and mark the letter A, B, C, D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.

Some people look at an equation and see a bunch of complicated numbers and symbols while others see beauty [I]. Now, thanks to a new tool created at Carnegie Mellon University, anyone can now translate the abstractions of mathematics into beautiful and instructive illustrations [II]. This exciting new tool is named Penrose after the mathematician Roger Penrose, who is famous for using diagrams and other drawings to communicate complicated mathematical ideas [III]. Penrose enables users to create diagrams simply by typing mathematical expressions and letting the software do the drawing [IV].

Unlike a graphing calculator, these aren’t restricted to basic functions, but can be complex relationships from any area of mathematics. “Some mathematicians have a talent for drawing beautiful diagrams by hand, but they vanish as soon as the chalkboard is erased,” said Keenan Crane, an assistant professor of computer science and robotics. “We want to make this expressive power available to anyone.”

Diagrams are often underused in mathematical communication, since producing high-quality illustrations is beyond the skill of many researchers and requires a great deal of time and effort. Penrose addresses these challenges by letting diagram-drawing experts turn their knowledge about creating diagrams into computer codes so that other users can access this capability using familiar mathematical language and a computer. “We started off by asking: ‘How do people translate mathematical ideas into pictures in their head?’” said Katherine Ye, a Ph.D. student in the Computer Science Department who is involved in the development of Penrose. “The secret sauce of our system is to empower people to easily ‘explain’ this translation process to the computer, so the computer can do all the hard work of actually making the picture.”

Once the computer learns how the user wants to see a mathematical object visualized – a vector represented by a little arrow, for instance, or a point represented as a dot – it uses these rules to draw several candidate diagrams. Users can then select and edit the diagrams they want from a gallery of possibilities. A special, simple-to-learn programming language was also developed so that they can easily convey the ideas in their minds to the Penrose system, Crane said. “Mathematicians can get very picky about notations,” he explained. “We let them define whatever notation they want, so they can express themselves naturally.”

The researchers will present Penrose at the SIGGRAPH 2020 Conference on Computer Graphics and Interactive Techniques, which will be held this July. “Our vision is to be able to dust off an old math textbook from the library, drop it into the computer and get a beautifully illustrated book - that way more people understand,” Crane said, noting that Penrose is a first step toward this goal.

(Adapted from sciencedaily.com)


Which of the following best summarizes paragraph 3?

Trả lời:

Trả lời:

Đáp án đúng:


Câu hỏi này thuộc đề thi trắc nghiệm dưới đây, bấm vào Bắt đầu thi để làm toàn bài

Câu hỏi liên quan

Lời giải:
Đáp án đúng: a
Lời giải:
Đáp án đúng: a
Câu 3:

Dear Michael,

a. I’m really grateful for your feedback; it gave me a fresh perspective.

b. Thanks for reviewing the draft of my article on environmental issues.

c. I’m making the necessary edits now and hope to submit it by the end of the week.

d. If you have time, maybe we can discuss the revisions over coffee.

e. I look forward to your thoughts on the updated version once it’s ready.

Best wishes,

Lily

Lời giải:
Đáp án đúng: a
Câu 4:

Having a daily routine really keeps me organized.

b. I start my day with a short meditation session followed by a healthy breakfast.

c. Then, I plan out my tasks and set aside time for each.

d. This helps me stay productive throughout the day without feeling overwhelmed.

e. In the end, I feel much more accomplished and balanced

Lời giải:
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Câu 5:

The local park has been renovated and now features a brand-new playground.

b. However, the increase in visitors has led to some littering issues.

c. Many families and children enjoy spending time there on weekends.

d. To address this, the city plans to install more trash bins and hire extra staff for maintenance.

e. Overall, it’s a great improvement, but keeping the park clean will require community effort

Lời giải:
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Câu 6:

Which of the following can be inferred from the passage?

Lời giải:
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Câu 7:

Read the following advertisement 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 1 to 6.

During the 1960s and '70s, industrialised countries suffered a(n) (1) ______ and violent crimes such as muggings increased at an alarming rate. What is more, it was expected to (2) ______ worse. Only it didn’t. Instead, it got much, much better. In the 1990s, crime started to fall dramatically, and today it is down by almost 50% across the industrialised world and continues to fall. Triumphant politicians will assert that their policies have cut crime. Actually, (3) ______ of the country’s policies, the trend does coincide (4) ______ the use and subsequent prohibition of tetraethyl lead in petrol, (5) ______ for years as a cause of aggressive behaviour. Therefore, countries that still use leaded petrol are being urged to stop (6) ______ it to help improve health and crime prevention.


During the 1960s and '70s, industrialised countries suffered a(n) (1) ______ and violent crimes such as muggings increased at an alarming rate
Lời giải:
Bạn cần đăng ký gói VIP để làm bài, xem đáp án và lời giải chi tiết không giới hạn. Nâng cấp VIP
Câu 7:

Read the following advertisement 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 1 to 6.

During the 1960s and '70s, industrialised countries suffered a(n) (1) ______ and violent crimes such as muggings increased at an alarming rate. What is more, it was expected to (2) ______ worse. Only it didn’t. Instead, it got much, much better. In the 1990s, crime started to fall dramatically, and today it is down by almost 50% across the industrialised world and continues to fall. Triumphant politicians will assert that their policies have cut crime. Actually, (3) ______ of the country’s policies, the trend does coincide (4) ______ the use and subsequent prohibition of tetraethyl lead in petrol, (5) ______ for years as a cause of aggressive behaviour. Therefore, countries that still use leaded petrol are being urged to stop (6) ______ it to help improve health and crime prevention.


What is more, it was expected to (2) ______ worse
Lời giải:
Bạn cần đăng ký gói VIP để làm bài, xem đáp án và lời giải chi tiết không giới hạn. Nâng cấp VIP