Cho mạch cộng không đảo như hình vẽ.

Cho biết các giá trị R₁ = R₂ = 1 kΩ, R_f  = R_g = 10 kΩ, U_{vào 1} = 1 V, U_{vào 2} = 5 V. Khi đó, điện áp U_ra có giá trị

Trong công thức tính tiết diện dây dẫn điện \({\rm{S}} = \frac{{\rm{I}}}{{\rm{J}}}\) thì J là 

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)

chọn đúng hoặc sai với mỗi ý a), b), c), d)

Ion nào sau đây có cấu hình electron giống nguyên tử neon (Ne)?

Trong sản xuất, kĩ thuật điện có vai trò

Trong không gian với hệ toạ độ Oxyz mặt cầu \({({\rm{x}} - 5)^2} + {({\rm{y}} + 8)^2} + {({\rm{z}} - 13)^2} = {9^2}\) có toạ độ tâm là 

Histidine là một trong những amino acid thiết yếu đối với cơ thể con người. Với mỗi môi trường có giá trị pH bằng 4, $0;7,6;12,0$, coi histidine chỉ tồn tại ở dạng cho dưới đây:

Trong quá trình điện di, ion sẽ di chuyển về phía điện cực trái dấu với ion.

Cho các nhận định sau về quá trình điện di của histidine:

     (a) Với môi trường $\text{pH}=7,6$ thì dạng (II) hầu như không dịch chuyển về các điện cực.

     (b) Với môi trường $\text{pH}=4,0$ thì dạng (I) di chuyển về phía cực âm.

     (c) Với môi trường $\text{pH}=12,0$ thì dạng (III) di chuyển về phía cực dương.

     (d) Với môi trường $\text{pH}=7,6$ thì dạng (II) di chuyển về phía cực âm.

Các nhận định đúng là