1
vote
0answers
9 views

Rotationmatrix for coordinate system

this is my first question with regard to mathematics. So, if I made any mistake in terms of naming and/or convention, please let me know. I'm having a little problem with rotating a coordinate system ...
0
votes
2answers
53 views

Rotation of Matrices and their interpretation

Given are now two matrices and I have to discuss what the given functions are doing (geometrically). Maybe you can revise/add the following: given are the matrices $ A = \begin{pmatrix} \cos(a) ...
1
vote
0answers
54 views

Writing a rotation as a product of translation and rotation about origin

In Artin's Algebra 2011 we have Lemma 6.3.5: "An isometry $f$ that has the form $m=t_a\rho_\theta$, with $\theta\neq 0$, is a rotation through the angle $\theta$ about a point in the plane." Earlier ...
1
vote
1answer
70 views

Rotation vs lift distance

I'm working on a homework problem and I think I found an answer, but not positive. Here is the question: A winch with a $6$-inch radius is used to lift a container. The winch is designed so that as ...
1
vote
2answers
149 views

manifold diffeomorphic (?) to SO(3)

Consider the set of all pairs $(\boldsymbol{n},\boldsymbol{v})$ of vectors in $\mathbb{R}^3$ such that $\boldsymbol{n}$ is a vector on the unit sphere centered at the origin and $\boldsymbol{v}$ is a ...
3
votes
2answers
108 views

Put a transformation under the form of a rotation in the complex plane

On the complex plane, I have a transformation "T" such that : $z' = (m+i)z + m - 1 - i$ ($z'$ is the image and $z$ the preimage, $z$ and $z'$ are both complex number) and $m$ is a real number. ...
1
vote
2answers
684 views

Finding the standard matrix of a reflection operator

I was working on an exercise in which I am given a vector (2,-1, 2) and I am supposed to find the standard matrix A of the reflection operator T on R3 such that T(v)=-v. Here's my attempt at the ...