Which of the following matrix should I use if I want to rotate a line by 30 degree?A. [1–√/2:3/2;3/2:1–√/2]B. [3–√/2:−1/2;1/2:3–√/2]C. [1–√/2:−1/2;1/2:1–√/2]D. [30 : -1/2; 1/2 : 30]
Question
Which of the following matrix should I use if I want to rotate a line by 30 degree?A. [1–√/2:3/2;3/2:1–√/2]B. [3–√/2:−1/2;1/2:3–√/2]C. [1–√/2:−1/2;1/2:1–√/2]D. [30 : -1/2; 1/2 : 30]
Solution 1
To rotate a line by 30 degrees, you would use a rotation matrix. The general form of a 2D rotation matrix is:
[cosθ -sinθ] [sinθ cosθ]
where θ is the angle of rotation. In this case, θ is 30 degrees.
First, convert 30 degrees to radians because the trigonometric functions in the rotation matrix use radians, not degrees.
30 degrees = 30 * π/180 = π/6 radians
Then, substitute π/6 into the rotation matrix:
[cos(π/6) -sin(π/6)] [sin(π/6) cos(π/6)]
which simplifies to:
[√3/2 -1/2] [1/2 √3/2]
So, the correct answer is B. [3–√/2:−1/2;1/2:3–√/2]
Solution 2
To rotate a line by 30 degrees, you would use a rotation matrix. The general form of a 2D rotation matrix is:
[cosθ -sinθ] [sinθ cosθ]
where θ is the angle of rotation. In this case, θ is 30 degrees.
First, convert 30 degrees to radians because the trigonometric functions in the rotation matrix use radians, not degrees.
30 degrees = 30 * π/180 = π/6 radians
Then, substitute π/6 into the rotation matrix:
[cos(π/6) -sin(π/6)] [sin(π/6) cos(π/6)]
which simplifies to:
[√3/2 -1/2] [1/2 √3/2]
So, the correct answer is B. [3–√/2:−1/2;1/2:3–√/2]
Similar Questions
Which of the following matrix should I use if I want to shift my line by 3 units in the X-axis and 4 units in the Y-axis?A. [3: 0 : 0; 0: 4: 0;0: 0: 1]B. [3 : 0; 0 : 4]C. none of the aboveD. [1 : 0 : 3; 0: 1: 4; 0: 0: 1]
Rotate Matrix by 90 Degrees
(c) Determine the concatenated transformation matrix for translation by vector [1 1] followed by rotation of 45 degrees in 2D square matrix of points given [-1,-1] [1,1] [1,-1] [-1,1]
Problem StatementHarish is developing a program for a robotics project that involves processing a 2D grid. The program requires rotating a 2D matrix 90 degrees clockwise in place.He needs to implement the rotateMatrix function to achieve this rotation without using any temporary arrays or data structures, only dynamic memory allocation. Additionally, he needs to provide functions to display the original and rotated matrices. Write a program to accomplish this task.Note: This kind of question will help in clearing HCL recruitment.Input format :The first line of the input consists of an integer 'n', which represents the size of the square matrix (n x n).The second part contains 'n x n' integers representing the elements of the matrix in row-major order.Output format :The first matrix is the original matrix.The second matrix is the matrix after a 90-degree clockwise rotation.Refer to the sample output for formatting specifications.Code constraints :1 <= n <= 100Sample test cases :Input 1 :31 2 34 5 67 8 9Output 1 :Original Matrix:1 2 3 4 5 6 7 8 9 Matrix after 90-degree clockwise rotation:7 4 1 8 5 2 9 6 3 Input 2 :-2Output 2 :Size of the matrix should be positive!Note :The program will be evaluated only after the “Submit Code” is clicked.Extra spaces and new line characters in the program output will result in the failure of the test case.
(c) Determine the concatenated transformation matrix for translation by vector [1 1] followed by rotation of 45 degrees in 2D as shown in Figure 2 below.
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