What Is the Line of Reflection for the Matrix Transformation f(v)?

Thread starter bookworm_07
Start date Oct 4, 2005
Tags

Geometry Reflection

AI Thread Summary

The discussion centers on finding the line of reflection for the matrix transformation f(v) defined by the given matrix. The transformation is shown to represent a reflection in a line L through the origin. To determine the line of reflection, one must identify a line L that remains fixed under the transformation f. Participants express difficulty in comparing the reflection formulas and identifying the fixed line. The key focus is on understanding the relationship between the matrix and the geometric reflection it represents.

Oct 4, 2005

bookworm_07

f(v) = (the matrix)
|cosx sinx |
|sinx -cosx |(v)

If x is in R and f: R^2 --> R^2
show that f is a reflection in a line L through the origin, and find the line of reflection.

im having trouble figureing this out, i know that i need to find a line L fixed by f, and then to compare the formulas for the reflection --> RL and f.
i just don't know what to do. Thank you.

Last edited: Oct 4, 2005

Physics news on Phys.org

Oct 4, 2005

bookworm_07

************

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...

View full post »

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...

View full post »

Thread 'Explain this asphalt sheen'

This problem is two parts. The first is to determine what effects are being provided by each of the elements - 1) the window panes; 2) the asphalt surface. My answer to that is The second part of the problem is exactly why you get this affect. And one more spoiler:

View full post »