PHẦN II. Thí sinh trả lời từ câu 1 đến câu 4. Trong mỗi ý a), b), c), d) ở mỗi câu, thí sinh chọn đúng hoặc sai.
Cho phương trình \(\tan x = \sqrt 3 .\)
a) Điều kiện xác định của phương trình \(x \ne \frac{\pi }{2} + k2\pi \,\,\left( {k \in \mathbb{Z}} \right)\).
b) \(x = \frac{\pi }{3}\) là một nghiệm của phương trình.
c) Tập nghiệm của phương trình là \(\left\{ {\frac{{2\pi }}{3} + k2\pi ;\frac{{ - 2\pi }}{3} + k2\pi |k \in \mathbb{Z}} \right\}.\)
d) Phương trình có hai nghiệm trên đoạn \(\left[ {0;2\pi } \right].\)
PHẦN II. Thí sinh trả lời từ câu 1 đến câu 4. Trong mỗi ý a), b), c), d) ở mỗi câu, thí sinh chọn đúng hoặc sai.
Cho phương trình \(\tan x = \sqrt 3 .\)
a) Điều kiện xác định của phương trình \(x \ne \frac{\pi }{2} + k2\pi \,\,\left( {k \in \mathbb{Z}} \right)\).
b) \(x = \frac{\pi }{3}\) là một nghiệm của phương trình.
c) Tập nghiệm của phương trình là \(\left\{ {\frac{{2\pi }}{3} + k2\pi ;\frac{{ - 2\pi }}{3} + k2\pi |k \in \mathbb{Z}} \right\}.\)
d) Phương trình có hai nghiệm trên đoạn \(\left[ {0;2\pi } \right].\)
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Nội dung nào dưới đây thể hiện phương pháp đảm bảo an toàn khi làm việc trong phòng thí nghiệm?
Read the following passage about Building Understanding Across Nations 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 23 to 30.
In our interconnected world, cultural ambassadors play a vital role in bridging the gaps between different nations and peoples. These dedicated individuals and groups serve as links between cultures, fostering mutual understanding and respect through various activities and programs. Their mission is to showcase their own cultural heritage while learning about and appreciating others, creating pathways for meaningful dialogue and lasting connections across borders.
Cultural ambassadors employ numerous methods to achieve their goals. They organize traditional festivals and art exhibitions that display unique customs, allowing visitors to experience different cultures firsthand. Language exchange programs enable people to communicate more effectively, while cultural workshops teach traditional crafts, music, and dance. These ambassadors also utilize digital platforms to reach wider audiences, sharing stories and traditions through social media and online events that connect people from different corners of the world.
Despite their important work, cultural ambassadors face several challenges in their mission. Stereotypes and prejudices can create barriers to understanding, while language differences sometimes lead to misunderstandings. Limited resources and funding may restrict their activities, and political tensions between nations can complicate their efforts. However, these dedicated individuals persist in their work, believing that personal connections and shared experiences can overcome these obstacles and promote harmony among different communities.
Looking ahead, the role of cultural ambassadors becomes increasingly significant in our global society. Their efforts to build bridges between nations contribute to reducing conflicts and fostering peace. Through their continued dedication to promoting cross-cultural understanding, these ambassadors help create a more inclusive and connected world where differences are celebrated rather than feared. This ongoing process of cultural exchange remains essential for building a future based on mutual respect and cooperation.
Which of the following is TRUE according to the passage?
Mark the letter A, B, C or D to indicate the best arrangement of utterances or sentences to make a meaningful exchange or text in each of the following questions from 13 to 17
a. Anna: Thank you so much for the compliment. I put a lot of effort into it, so it's great to hear that it's appreciated.
b. Bean: Wow, this report is amazing! You did an excellent job on the research and the writing is very clear.
c. Anna: I just submitted my report on ASEAN. I'm hoping to get a good grade on it.
Năng lượng vật dao động điều hòa
Complete the following sentences with the correct forms of the words in capitals
He was a worthy _______________________ of the Nobel Prize. (RECEIVE)
- Hình bên mô tả thí nghiệm về hiện tượng cảm ứng điện từ. Khi tăng tốc độ di chuyển thanh nam châm, dòng điện trong ống dây
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)
Where in paragraph 1 does the following sentence best fit?
For many, the elegance of mathematical concepts often goes unnoticed amidst
the complexity.
Thành phần kinh tế Nhà nước có vai trò
Cặp số (1; 0) là một nghiệm của hệ:
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Choose the word that has the underlined part pronounced differently from the others.
Trong các chất: Khí O2, CO2, carbohydrate, H2O. Có bao nhiêu chất là nguyên liệu của quá trình quang hợp?
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Để giảm thiểu phát thải các khí nhà kính, Hoa Kì chú ý biện pháp gì?
Đại biểu Hội đồng nhân dân có trách nhiệm gì với cử tri?
