Question

MATLAB

2. a. Create the vector G- b. Compute the counter-clockwise rotations of the vector a, at angles 45, 90, 130, and 180 degrees using the 2 x 2 rotation matrices. Store all 4 of these results with variable names a-45, a-90, a-130, and a_180. c. On the same figure, using the function plot, plot all 5 vectors a, a-45, a_90, a 130, and a 180, each vector with a different color. You may choose different line styles, but this part is op- tional. d. Add a title of your choice and add axes labels.

Answer 1

clear
clc
a=[1;0];
R=@(th)[cosd(th) -sind(th);sind(th) cosd(th)];
a_45=R(45)*a
a_90=R(90)*a
a_130=R(130)*a
a_180=R(180)*a

plot([0 a(1)],[0 a(2)],'r')
hold on
plot([0 a_45(1)],[0 a_45(2)],'g')
plot([0 a_90(1)],[0 a_90(2)],'m')
plot([0 a_130(1)],[0 a_130(2)],'b')
plot([0 a_180(1)],[0 a_180(2)],'k')
legend('a','45\circ','90\circ','130\circ','180\circ')
axis([-2 2 -2 2])

xlabel('x')
ylabel('y')
title('Rotated lines')