Tính góc tạo bởi giữa hai đường thẳng
\({{d}_{1}}:2x-y-10=0\) và \({{d}_{2}}:x-3y+9=0.\)
\({{30}^{\text{o}}}.\)
\({{45}^{\text{o}}}.\)
\({{60}^{\text{o}}}.\)
\({{135}^{\text{o}}}.\)
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
Ta có
\(\left\{ \begin{align} & {{d}_{1}}:2x-y-10=0\to {{{\vec{n}}}_{1}}=\left( 2;-1 \right) \\ & {{d}_{2}}:x-3y+9=0\to {{{\vec{n}}}_{2}}=\left( 1;-3 \right) \\ \end{align} \right.\)
\(\xrightarrow{\varphi =\left( {{d}_{1}};{{d}_{2}} \right)}\cos \varphi =\frac{\left| 2.1+\left( -1 \right).\left( -3 \right) \right|}{\sqrt{{{2}^{2}}+{{\left( -1 \right)}^{2}}}.\sqrt{{{1}^{2}}+{{\left( -3 \right)}^{2}}}}=\frac{1}{\sqrt{2}}\)
\(\to \varphi ={{45}^{\circ }}.\)
Chọn B.
Bộ Đề Kiểm Tra Giữa Học Kì I - Toán 10 - (Năm 2023 - 2024) - Các Trường THPT Trên Toàn Quốc là tài liệu giúp học sinh hệ thống lại các kiến thức đã học thông qua các câu hỏi ngắn gọn và súc tích. Các bài tập được thiết kế phù hợp với nhiều đối tượng học sinh, từ cơ bản đến nâng cao.
Câu hỏi liên quan
Thông tin của thị trường giúp người mua điều gì?
Read the following passage about studying abroad 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.
Successful students often do the followings while studying. First, they have an overview before reading. Next, they look for important information and pay greater attention to it (which often needs jumping forward or backward to process information). They also relate important points to one another. Also, they activate and use their prior knowledge. When they realize that their understanding is not good, they do not wait to change strategies. Last, they can monitor understanding and take action to correct or “fix up” mistakes in comprehension.
Conversely, students with low academic achievement often demonstrate ineffective study skills. [I] They tend to assume a passive role in learning and rely on others (e.g., teachers, parents) to monitor their studying. [II] For example, low-achieving students often do not monitor their understanding of content; they may not be aware of the purpose of studying; and they show little evidence of looking back or employing “fix-up” strategies to fix understanding problems. [III] Students who struggle with learning new information seem to be unaware that they must extend effort beyond simply reading the content to understand and remember it. [IV]
Children with learning disabilities do not plan and judge the quality of their studying. Their studying may be disorganized. Students with learning problems face challenges with personal organization as well. They often have difficulty keeping track of materials and assignments, following directions, and completing work on time. Unlike good studiers who employ a variety of study skills in a flexible yet purposeful manner, low-achieving students use a restricted range of study skills. They cannot explain why good study strategies are important for learning; and they tend to use the same, often ineffective study approach for all learning tasks, ignoring task content, structure or difficulty.
Which of the following is TRUE about students with low academic achievement, according to the passage?
Biết khối lượng của các hạt proton, neutron và hạt nhân \(_{11}^{23}{\rm{Na}}\) lần lượt là \(1,0073{\rm{u}};1,0087{\rm{u}};\) và \(22,9838{\rm{u}}.\) Năng lượng liên kết của hạt nhân \(_{11}^{23}{\rm{Na}}\) là
Có bao nhiêu số gồm 3 chữ số khác nhau được thành lập từ các chữ số 0, 2, 4, 6, 8 ?
Kết quả của các cuộc cách mạng tư sản là gì?
Đâu năng lượng chủ yếu được tạo ra từ quá trình hô hấp?
a. Jessica: Me too. I have to wash the dishes and clean my room.
b. William: My parents expect me to help around the house.
c. William: It's a good thing, though. It helps me learn responsibility.
Read the following passage about the Science in Service of Humanity 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 has come out of its shell in laboratories to become a powerful force for human advancement. Modern scientific endeavors increasingly focus on addressing real-world challenges affecting communities globally. From developing vaccines that save millions to creating technologies connecting people across continents, science serves humanity in countless ways. This shift represents a fundamental evolution in how we perceive scientific progress—not merely academic pursuit but a practical tool for improving lives and solving pressing problems.
[I] Medical breakthroughs exemplify how science directly benefits humanity. [II] For instance, gene therapy offers hope for those with inherited conditions, while artificial intelligence helps diagnose diseases earlier and more accurately. [III] These advancements didn't happen overnight; scientists had to burn the midnight oil for years before achieving success. [IV] Their perseverance demonstrates that when science targets humanitarian goals, results can transform society profoundly.
Environmental science has emerged as another crucial domain where laboratory work translates into human welfare. Climate scientists provide data informing policy decisions affecting billions. Conservation biologists develop strategies to protect biodiversity, ensuring future generations benefit from natural resources. Agricultural researchers create drought-resistant crops helping communities withstand changing climate conditions. Despite these contributions, environmental science faces challenges including funding limitations, political resistance, and urgency of addressing accelerating climate change. Nevertheless, dedicated scientists continue their work, recognizing environmental health directly impacts human wellbeing.
The future of science in service of humanity looks increasingly collaborative and inclusive. Modern approaches incorporate diverse perspectives, including indigenous knowledge and community participation. Citizen science projects engage non-professionals in data collection, democratizing the scientific process. Open-access publishing makes research findings available to anyone with internet access, not just wealthy institutions. These developments suggest science's greatest potential lies in becoming more accessible and responsive to human needs. As we face complex global challenges, from pandemics to climate change, science serving humanity offers our best hope for a sustainable future.
Which of the following best paraphrases the underlined sentence in paragraph 4?
Quốc hội thực hiện chức năng gì?
Mark the letter A, B, C or D on your answer sheet 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. Alex: Hey Jamie, do you have any plans for the weekend?
b. Alex: That sounds like a great idea! Where should we go?
c. Jamie: Not yet! I was thinking we could go on a little adventure. What do you think?
Một người nghe thấy tiếng sét sau tia chớp 5 giây. Hỏi người đó đứng cách nơi xảy ra sét bao xa? Biết vận tốc truyền âm trong không khí là 340m/s.
Đâu KHÔNG phải là giá trị nội dung của bài thơ Đò Lèn (Nguyễn Duy)?
Cơ cấu ngành kinh tế của Cộng hòa Nam Phi có sự chuyển dịch nào sau đây?
Mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the following questions:
She is a(n) _________ . She finds it difficult to socialize with other students in the class.
Xác định ý đúng: Chức năng của phân bón?
Cho hai tập A = [0; 5] B = (2a; 3a + 1), a > –1. Với giá trị nào của a thì \[{\rm{A}} \cap {\rm{B}} \ne \emptyset \].
Đồng vị phóng xạ (60Co) phát ra tia γ có khả năng đâm xuyên mạnh, dùng điều trị các khối u sâu trong cơ thể. Cobalt có ba đồng vị 2759Co (chiếm 98%), 2758Co và 2760Co, nguyên tử khối trung bình là 58,982. Xác định hàm lượng phần trăm của đồng vị phóng xạ 60Co.
Năm 1077, quân dân nhà Lý kháng chiến thắng lợi hoàn toàn chống quân xâm lược nào?
Ý nào sai khi nói về protein xuyên màng?
Choose A, B, C or D to make a complete dialogue for each question.
a. Well, we can’t deny this. I’ve started using paper bags exclusively. It’s my small way of helping the environment.
b. Do you ever consider using paper bags instead of plastic?
c. No, I find it easier to just reuse the plastic ones I already have at home.
d. I agree, but aren’t plastic bags still more convenient for carrying heavier items?
e. Surely. But have you noticed how plastic bags pile up and become a problem?
f. I haven’t really thought about it, but maybe it’s time to switch to paper.