Why doesn't this code rotate and transform the spiral?

clear
clc
clf
t = linspace( 0,4*pi,1000)
r=@(t) sqrt(t)

x=  r(t).*cos(t)
y= r(t).*sin(t)

plot(x,y)

%turns x and y into a 3xn matrix
pts=[x;y;ones(1,length(x))]

%create matrix
mTrans=eye(3,3);
%declare translation variables
dx=5;
dy=1.5;
%apply to matrix
mTrans(1,3)=dx;
mTrans(2,3)=dy;

%create matrix
mRot=eye(3,3);
%define rotation angle
theta=pi/6;
%change matrix
mRot(1,1)=cos(theta);
mRot(1,2)=sin(theta);
mRot(2,1)=-sin(theta);
mRot(2,2)=cos(theta);

%new points after tranformation and rotation
ptsNew=mTrans*mRot*pts

hold on 
plot(pts)

Answer 1

[Stephan]

No for loop is needed:

t = linspace( 0,4*pi,1000);
r=@(t) sqrt(t);
x =  r(t).*cos(t);
y = r(t).*sin(t);
plot(x,y)
%turns x and y into a 3xn matrix
pts=[x;y;ones(1,length(x))];
%create matrix
mTrans=eye(3);
%declare translation variables
dx=5;
dy=1.5;
%apply to matrix
mTrans(1,3)=dx;
mTrans(2,3)=dy;
%define rotation angle
theta=pi;
%rotation matrix
mRot = [cos(theta), -sin(theta), 0; sin(theta), cos(theta), 0; 0, 0, 1];
%new points after tranformation and rotation
ptsNew=mTrans*mRot*pts;
hold on 
plot(ptsNew(1,:),ptsNew(2,:))
hold off

Answer 2

[darova]

Because you have to mulptiply each set of point separately

ptsNew = zeros(size(pts));
for i = 1:1000
    ptsNew(:,i) = mTrans*mRot*pts(:,i);
end
hold on 
plot(ptsNew(1,:),ptsNew(2,:))
hold off