Question

please help me.. urgent
This is compound transformations

B= a rotation about the origin of 45 degree
c=a stretch by a factor of 2 parallel to 0y-axis

find matrix operators for c followed by B

Answer 1

Here is the matrix for the rotation about the origin counterclockwise by an angle theta\[B=\left[\begin{matrix}\cos\theta & -\sin\theta \\ \sin\theta & \cos\theta\end{matrix}\right]\]here is what I think they mean by a stretch parallel to y by 2(I suppose they mean to stretch x)\[C=\left[\begin{matrix}2 & 0 \\ 0 & 1\end{matrix}\right]\]I have to get to class, no time to explain the derivation,so here is a link

http://tutorial.math.lamar.edu/Classes/LinAlg/LinearTransExamples.aspx

Answer 2

ok nvm u can answer this when u get back from class..

i dont understand how did u determine that it is clockwise or counter clockwise...

Answer 3

haha, no class after all
I don't know the holidays in this country very well yet
ok, derivation time...

Answer 4

take a point described by a vector of length r at an angle phi\[v=(x,y)\]from trigonometry we know that\[x=r\cos\phi\]\[y=r\sin\phi\]now we want to rotate this vector by an angle theta counterclockwise...

Answer 5

forgot to mark r on the other drawing:again from trig we know the components of the new transformed vector w will be\[w_1=r\cos(\phi+\theta)\]\[w_2=r\sin(\phi+\theta)\]now we can use the identity for the cosine and sine of the sum of two angles