How can I rotate, scale and transform x y z coordination.

I want to do coding for following equations. How i do it using mat lab. Please help me.

Answer 1

[KSSV]

clc; clear all ;
% square coordinates 
Sx = [0 1 1 0 0] ;
Sy = [0 0 1 1 0] ;
S = [Sx' Sy'] ;
% Rotation 
th = linspace(0,2*pi) ;
for i = 1:length(th)
    R = [cos(th(i)) sin(th(i)) ; -sin(th(i)) cos(th(i))] ;
    Sr = S*R ;
    plot(S(:,1),S(:,2),'b')
    hold on
    plot(Sr(:,1),Sr(:,2),'r')
    hold off
    drawnow
    pause(0.1)
end

[Dumi]

Thank you loads dr. Dr. Siva Srinivas. . I am getting x, y, z coordinates from arduino serial monitor. now i want to pre-process that data. So i want to normalized that data. so i am going to use that equations. So can I use your code for that. because my x y z coordinates are variables. Thank you. Please help me

[KSSV]

Procedure would be same, but for 3D you need to extend R, for 3D R would be 3x3.

Refer the following for R matrice sin 3D.

https://en.wikipedia.org/wiki/Rotation_matrix

Eg.

R = [1 0 0 ; 0 cos(th) -sin(th) ; 0 sin(th) cos(th)] ;

[Dumi]

Thank you again Dr . Siva Srinivas. I dont want 3D. sorry it is mistake. I only need x y coordinate. Is there answer for all 3 equations which I have attach. Thank you loads. I will try these. Thank you again.