1. Find the standard matrix for a counterclockwise rotation about the origin through 45°, followed by the orthogonal projection onto the y-axis.
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- Find the rotation matrix that could be used to rotate the vector by –20° about the origin. Take positive angles to be anticlockwise.b) Write the 3D Rotation Matrix around the y-axis by 0 = 45°: Rows: 3 Columns: 30Determine the matrix that can be used to define a rotation through pi about the point (2, -1). Find the image of the point (2,1) under this rotation.
- Q1. Consider the 3D shape with the following vertices: 4-38-60-60-98-88-8 A=5,B=5,C = 5,D = 5,E = 6,F= Rotate the 3D object by 30° (clockwise) at point D (fixed point) about the x-axis and then perform a uniform 1.5 scale. You should use rotation matrices.Derive the composite matrix for rotation about arbitrary point (a,b) in clockwise direction with angle (θ).Find the transformation matrix of the symmetrical transformation of the plane graph to the general position line x + y + 2=0 (write out the transformation process).
- Find the image of the vector (1, 1, 1) for the given rotation.b) Based on Figure 2 below, explain the process if we want to transform the cow as in figure (with vector B) from origin (with the cow facing to z-axis at 0,0,0). You only need to describe the process of transformation; you do not need to write down the matrix and its calculation. B(i) Find the matrix that represents the reflection g in the line through the origin with angle of inclination 165°. (ii) The matrix that represents the rotation h through 90° about the origin is 0 (i-1) Show that the composite transformation formed from the rotation h followed by the reflection g is the reflection in the line y = -√3x.
- 2B11. a) Let R correspond to a right-hand rotation of angle about the x3-axis. (a)Find the matrix of R². (b)Show that R² corresponds to a rotation of angle 20 about the same axis. (c)Find the matrix of R" for any integer n.Find the transformation matrix R that describes a rotation by 60° about an axis from the origin through the point (1, 1, 1). The rotation is counterclockwise as you look down the axis toward the origin. Help me fast so that I will give good rating.Find the Jacobian of the transformation = 2u + 7v, y=u² - 5v.
