Goal: Rotate a vector v = (x; y; z) about a general axis with direction vector (assume is a unit vector, if not, normalize it) by an angle (see gure 9.1).

Recall that every linear transformation R. = 67 ... given by rotating by radians (in the counter-clockwise direction about ~0). That is, for each vector ~v in R2, R(~v) is the result of rotating …

Examples Question 2: Rotate each of the shapes below as instructed, using the origin, (0,0), as the centre of rotation. Question 3: Rotate each of the shapes below as instructed. Question 4: …

R 1 = R Proof: As discussed at the bottom of page 259, the rotation R0 is a rotation by an angle of 0, which means R0 doesn't rotate anything at all. It's the identity function on the plane.

We show in this note how one can quickly rotate any figure F(x,y)=0 in 2D by any desired angle θ by simple matrix manipulations. Out starting point is to consider two orthogonal Cartesian …

Rotate the Triangles Graph the image of each triangle after rotating it about the origin.

For the three-bit rotate left (rol) shown above, the three left-most bits are shifted off the left side of the data word, but immediately appear as the three right-most bits, still in the same sequence, …