Trong không gian \(Oxyz\), cho hai điểm \(A(5;2;1), B (1;0;-1)\). Phương trình của mặt cầu đường kính \(AB\) là:
\((x-3)^2 + (y-1)^2 + z^2 = 6\).
\((x+3)^2 + (y+1)^2+(z+1)^2 = 20\).
\((x+3)^2 + (y+1)^2 + z^2 = 6\).
\((x+3)^2 + (y+1)^2 + z^2 = \sqrt{{6}}\).
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
Gọi \(I\) là trung điểm của \(AB\). Suy ra \(I (3;1;0)\).
Có \(I A=\sqrt{(5-3)^2+(2-1)^2+1^2}=\sqrt{6}\).
Mặt cầu đường kính \(A B\) có tâm \(I(3 ; 1 ; 0)\) và bán kính \(R=\sqrt{6}\) có phương trình là: \((x-3)^2+(y-1)^2+z^2=6\).
Bộ Đề Kiểm Tra Tham Khảo Học Kì II - Toán 12 - Cánh Diều – Bộ Đề 01 giúp học sinh ôn luyện chuyên sâu theo định hướng thi cuối cấp. Đề thi có 3 phần theo cấu trúc mới nhất: Phần A. Trắc Nghiệm, bao gồm Câu Trắc Nghiệm Nhiều Phương Án Lựa Chọn, Câu Trắc Nghiệm Đúng Sai, Câu Trắc Nghiệm Trả Lời Ngắn. Các nội dung chính được kiểm tra bao gồm: Ứng Dụng Đạo Hàm Để Khảo Sát Và Vẽ Đồ Thị Của Hàm Số, Nguyên Hàm, Tích Phân, Phương Pháp Tọa Độ Trong Không Gian, Phân Tích Và Xử Lí Dữ Liệu, Xác Suất. Câu hỏi được xây dựng với mức độ phân hóa hợp lý, phù hợp cho cả kiểm tra giữa kỳ và chuẩn bị thi tốt nghiệp THPT.
Câu hỏi liên quan
Cho hàm số \(f(x)=x^{3}-3 x^{2}+(k-2) x+1\).
Để đồ thị hàm số \(f(x)\) cắt trục \(O x\) tại 3 điểm phân biệt có hoành độ lập thành cấp số cộng thì \(k\) thuộc khoảng nào dưới đây?
Choose A, B, C or D that has the CLOSEST meaning to the given sentence in each question.
The increasing popularity of social media platforms has raised concerns about their potential negative effects on young people's mental health.
Ý nào dưới đây là thể hiện đặc điểm của mô hình sản xuất kinh doanh hợp tác xã?
Chọn đáp án đúng. Cho a, b là các số thực dương. Giá trị của \(\ln \frac{a}{b} + \ln \frac{b}{a}\) bằng?
Vì sao Nguyễn Dữ lại cáo quan về ở ẩn?
Cho cấp số nhân \(\left(u_{n}\right)\) thỏa mãn \(2\left(u_{3}+u_{4}+u_{5}\right)=u_{6}+u_{7}+u_{8}\).
Tính \(\frac{u_{8}+u_{9}+u_{10}}{u_{2}+u_{3}+u_{4}}\)
- Một vật chuyển động thẳng nhanh dần đều với vận tốc đầu = 18 km/h. Sau 10 s, vật đạt vận tốc 15 m/s. Gia tốc của vật là
Read the following passage about endangered languages and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questionsfrom 31 to 40.
[I] Social media has become a dominant force in modern communication, offering a range of benefits and challenges. [II] It has revolutionized the way people interact, share information, and even form relationships. [III] While these platforms offer opportunities for connection and expression, they also have their drawbacks. [IV] For instance, excessive use of social media has been linked to a range of negative effects, including mental health issues, social isolation, and decreased productivity. [V] However, when used responsibly, social media can also offer a variety of positive outcomes, such as the ability to stay connected with loved ones, network professionally, and access valuable information and resources.
One of the major benefits of social media is its ability to keep people connected. For example, individuals who live far apart can maintain close relationships through regular communication on these platforms. Social media also facilitates professional networking, allowing users to connect with potential employers or clients, and enabling companies to promote their products and services to a global audience. Additionally, platforms like Facebook, Twitter, and Instagram provide a space for people to share ideas, opinions, and creative work, fostering a sense of community and collaboration.
Despite these advantages, there are serious concerns about the negative impact of social media, particularly on mental health. Studies have shown that excessive social media use can contribute to feelings of anxiety, depression, and loneliness. This is often attributed to the unrealistic portrayals of life that are commonly shared on these platforms, leading to comparisons that can make individuals feel inadequate or left out. Furthermore, constant exposure to negative news or online bullying can exacerbate these feelings and contribute to long-term psychological stress.
Another issue with social media is its potential to distract people from their daily responsibilities. With notifications constantly popping up and endless streams of content to scroll through, individuals may find it difficult to focus on tasks such as work, school, or personal obligations. This can result in decreased productivity and a lack of attention to important matters.
Ultimately, the impact of social media depends on how it is used. If individuals are mindful of their usage patterns and take steps to limit their time on these platforms, they can enjoy the benefits of staying connected and informed without the negative consequences. Parents, educators, and mental health professionals can also play a role in helping young people develop healthy habits and manage their social media use effectively.
Which of the following best paraphrases the underlined sentence in paragraph 1?
“Social media has become a dominant force in modern communication."
Dùng thông tin sau cho Câu 37 và Câu 38: Biết độ lớn cảm ứng từ do một dây dẫn thẳng dài mang dòng điện I tạo ra ở vị trí cách trục dây dẫn một khoảng r là \(B = 2,{0.10^{ - 7}}\left( {\frac{I}{r}} \right),\) với B tính bằng tesla (T), r tính bằng mét (m) và I tính bằng ampe (A).
Từ trường cách một dây thẳng dài 40 cm có độ lớn cảm ứng từ là \(B = {10^{ - 6}}\;{\rm{T}}.\) Cường độ dòng điện trong dây là bao nhiêu ampe?
CHỦ ĐỀ: TRỞ VỀ
(Tham khảo bài văn của chủ đề trong đường link dưới đây ở trang 21)
https://tvsthpt.dlib.vn/app/doc-sach-ebook/d00ddd794efd
Và trả lời câu hỏi sau:
Theo đoạn [2], vợ Tâm muốn về thăm nhà ở quê cùng chồng.
Đúng hay sai?
Read the following passage about the Exploring The Universe 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.
Science is a vast and fascinating field that seeks to understand the natural world and the universe beyond[I]. It encompasses various disciplines, including physics, chemistry, biology, and astronomy[II]. Each of these areas contributes to our understanding of complex phenomena, [III]. For instance, scientific research has led to significant breakthroughs in medicine, renewable energy, and environmental conservation[IV]. In this essay, we will explore the impact of science on our lives, particularly focusing on space exploration.
One of the most intriguing aspects of science is space exploration. Humans have always looked to the stars, wondering what lies beyond our planet. The launch of satellites and manned missions has allowed us to gather valuable information about the cosmos. For example, NASA's Mars Rover has provided insight into the potential for life on other planets. Through meticulous research and data collection, scientists can analyze soil samples and atmospheric conditions, paving the way for future explorations.
Space exploration also raises critical questions about our existence and the future of humanity. As we continue to advance technologically, the prospect of colonizing other planets becomes more plausible. This endeavor could serve as a solution to the challenges we face on Earth, such as overpopulation and resource depletion. However, ethical considerations must guide these efforts. We must ensure that we do not repeat the mistakes of history, such as the exploitation of natural resources and indigenous populations.
Moreover, scientific advancements have enabled us to develop technologies that enhance our understanding of the universe. Telescopes and space probes allow us to observe distant galaxies, study black holes, and uncover the mysteries of dark matter. Each discovery leads to new questions, further fueling our curiosity and drive for knowledge. The concept of the multiverse, for instance, challenges our understanding of reality and pushes the boundaries of scientific thought.
In addition to exploring the universe, science plays a crucial role in addressing pressing issues on Earth. Climate change, for example, is a significant concern that scientists are actively investigating. Through climate models and data analysis, researchers can predict future trends and propose solutions to mitigate the effects of global warming. Public awareness and education are essential in fostering a collective response to environmental challenges.
As we reflect on the wonders of science, it is clear that its contributions extend far beyond mere knowledge acquisition. Science empowers us to make informed decisions about our health, environment, and future. By fostering a culture of curiosity and critical thinking, we can inspire future generations to continue exploring the unknown.
Where in paragraph 1 does the following sentence best fit?
enabling advancements that improve our daily lives
Nguyên tử nguyên tố X có 4 lớp electron. Lớp thứ 3 có 14 electron. Số hiệu nguyên tử của nguyên tố X là
Cho hàm số \(f\left( x \right)\) xác định và có đạo hàm đến cấp hai trên \(\mathbb{R}\), thỏa mãn phương trình
\({{\left( {f}'\left( x \right) \right)}^{2}}+f\left( x \right)\cdot {f}''\left( x \right)=\) \(20{{x}^{4}}+12{{x}^{2}}+9,\forall x\in \mathbb{R}\) và \(f\left( 0 \right)=0\).
Biết rằng vế trái của phương trình có thể biểu diễn dưới dạng đạo hàm của một hàm số.
Mỗi phát biểu sau là đúng hay sai?
- Trong mỗi ý a), b), c), d) ở mỗi câu, thi sinh chọn đúng hoặc sai
Trong không gian với hệ toạ độ Oxyz, cho đường thẳng \(\Delta :\frac{{{\rm{x}} - 2024}}{1} = \frac{{{\rm{y}} - 2025}}{{ - 1}} = \frac{{{\rm{z}} - 2026}}{{\sqrt 2 }}\)
và mặt phẳng \(({\rm{P}}):{\rm{x}} + {\rm{y}} - \sqrt 2 {\rm{z}} - 2025 = 0.\)
Nơi nào diễn ra sự bào mòn, rửa trôi đất đai mạnh nhất?
Chọn ý đúng: Nhân tố quan trọng nhất góp phần mở rộng thị trường của hoạt động ngoại thương ở các nước trên thế giới hiện nay?
Mọi hành vi vi phạm quyền bất khả xâm phạm về thân thể của mỗi công dân đều sẽ:
Cho các nguyên tử sau: B (Z = 8, A = 16), D (Z = 9, A = 19), E (Z = 8, A = 18), G (Z = 7, A = 15). Trong các nguyên tử trên, các nguyên tử nào thuộc cùng một nguyên tố hoá học?
Read the following passage about the impact of social media on mental health and mark the letter A, B, C, or D on your answer sheet to indicate the best answer to each of the following questions
[I] In recent years, social media platforms have become a central part of daily life, offering users countless ways to connect, share, and communicate. [II] While these platforms offer many advantages, experts have noted rising concerns about their effects on mental health, particularly among young people (Smith & Anderson, 2018). [III] Studies reveal that excessive social media use can contribute to feelings of anxiety, depression, and loneliness, despite its intention to promote connection and social interaction (Twenge & Campbell, 2019). [IV]
A primary reason for these mental health concerns is the tendency for social media users to compare themselves to others. Platforms like Instagram and Facebook often highlight idealized lifestyles, leading users to feel inadequate about their own lives. Additionally, the constant notifications and messages contribute to a "fear of missing out," or FOMO, which keeps individuals in a cycle of checking their phones, often reducing the quality of sleep and overall well-being.
There is also a growing body of research suggesting a link between social media use and decreased attention spans. When users frequently switch between apps and notifications, their ability to focus for extended periods may diminish (Rosen, 2019). This shift in attention can interfere with productivity, especially in academic and professional settings, where sustained focus is essential.
Addressing these challenges requires a multi-faceted approach. Some mental health professionals suggest limiting screen time and setting boundaries, such as "device-free" hours before bedtime. Others recommend engaging in offline activities, like reading or exercising, to reduce dependence on social media and build healthier habits. According to psychologists, such strategies can bu mental resilience and allow for more meaningful, balanced relationships (Robinson & Smith, 2020).
Where in paragraph I does the following sentence best fit? “Young people are particularly affected due to their high engagement with these platforms.”
Đọc đoạn trích sau và trả lời câu hỏi:
Thuở nhỏ tôi ra cống Na câu cá
níu váy bà đi chợ Bình Lâm
bắt chim sẻ ở vành tai tượng Phật
và đôi khi ăn trộm nhãn chùa Trần.
(Đò Lèn, Nguyễn Duy)
Xác định phương thức biểu đạt chính được sử dụng trong đoạn thơ trên.
