# rotations

1. ### Rotations of a shape

after plotting the points (3,3) (-2,2) (-3-3) and (2-2) and joining the points on the graph I have constructed a quadrilateral shape, I am trying to figure the elements of the symmetry group of this shape, so far I have the identity element and a rotation about pi , I cant seem to find any...
2. ### Planar line translation and rotations...

We have planar lines in the form of $X=tP+sQ$, where $P$ and $Q$ are two fixed different points and $s,$ $t$ are varying reals satisfying $s+t=1$. We need to find the formula for the images of the line $X=tP+sQ$ in the following three cases: 1. Under the translation by a vector B. 2. Under...
3. ### Determine the matrices that represent the following rotations of R^3

I need to determine the matrix that represents the following rotation of $R^3$. (a) angle $\theta$, the axis $e_2$ (b) angle $2\pi/3$, axis contains the vector $(1,1,1)^t$ (c) angle $\pi/2$, axis contains the vector $(1,1,0)^t$ Now, I would like to check if I got the right answers...
4. ### equivalent rotations

I have two sets of three non-collinear unit vectors which are the axes of rotation in the 3d cartesian system. The problem is how to calculate for the given rotations (alpha, beta, gamma) in the first set equivalent rotation angles in the second one? I suppose that we should take into account...
5. ### Translations, Rotations and Reflections

Draw and label with triangle LMN with L (2, -1),M (3,1),N(4,-2) Triangle LMN is translated by the vector -2 Draw and label triangle L1M1N1 7 Triangle LMN is rotated 90 degrees clockwise about the origin. Draw and label triangle L2M2N2 Triangle LMN is enlarged by a scale of 2...
6. ### rotations of points

Hi Can anyone explain this following example to me? I have no idea how they obtained those new coordinates. How exactly do I multiply the point A by the rotation matrix? Thanks
7. ### rotations

hi, i need to describe the rotations for C and D from the clear triangle. i have tried many way but i am unable to find out how to do this so i was looking for some help! thanks
8. ### Rotations in Complex plane

The cyclic group C_{n} is the group of n rotations that maps a regular n-gon onto itself. These rotations correspond to multiplying C by which n complex numbers?
9. ### Fixed point in rotations

I've drawn a picture and I think I know what the method is: \text{Rot}(P, \alpha)(S)=\begin{pmatrix}{\cos \alpha & \sin \alpha \\ \sin \alpha & -\cos \alpha \end{pmatrix} \begin{pmatrix}{s_1-p_1 \\ s_2-p_2} \end{pmatrix}+ \begin{pmatrix}{p_1 \\ p_2} \end{pmatrix} \text{Rot}(Q...
10. ### Conjugacy classes of Rotations and Dihedral groups

How do you find the conjugacy classes of rotations and dihedral groups... I dont even know where to begin... for eg. Conjugacy classes of: R8 ={1}, {r}, {r^2}, {r^3}, {r^4}, {r^5}, {r^6}, {r^7} and D4= {1}, {r^2}, {r; r^3}, {fr; rf}, {f; fr^2}. please explain in detail and from the...
11. ### Calculating Latitude/Longitude from Matrix3D rotations

I am using matrix rotations to rotate a world sphere in front of a static camera. I want to know the latitude and longitude of the point directly beneath the camera. I'm appending rotation on the Z axis to 'turn' left and right and appending rotations on the X axis to move...
12. ### Converting Matrix3D rotations to Latitude Longitude

I am using matrix rotations to rotate a world sphere in front of a static camera. I want to know the latitude and longitude of the point directly beneath the camera. I'm appending rotation on the Z axis to 'turn' left and right and appending rotations on the X axis to move forward/backward...
13. ### Give an example of rotations do not always commute in plane

Give an example of t wo rotations in the plane which proves that rotations do not always commute.
14. ### Compositions of rotations, glide reflections, etc

Let A = (0,0), B = (1,0), C = (1,1), D = (0,1), P=(.5,.5). Identity the following R_{B,\frac{\pi}{2}} \circ \gamma_{DC} R_{D,\frac{\pi}{2}} \circ \gamma_{DC} \gamma_{CB}\circ \gamma_{DC} For the first one, I eventually got \gamma_{D'K'} where D'= (0, .5) and K'=(-.5,0), but I don't think...
15. ### Finding angle of rotation. Test this Monday. I missed school. Seriously need help.

Ok. Here is what i do know: in an equation: Ax² + Bxy + Cy² + Dx + Ey + F = 0 i need to eliminate the Bxy part, and find an angle of rotation. cot(2Ɵ) =(a-c)/b from there i can find Ɵ and create a new x',y' equation without a Bxy part. Here is my question: when there are 2 possible values for...
16. ### Identifying translations and rotations

Given the following diagram (note that the intersection point of the segment that connects triangles XYB and ABC on the segment AB should be point I), where the triangles are all equilateral, and the points H, I, and J bisect the segments AC, AB, and XB, respectively: Identity the following...