Linear transformation rotation

[fk378]

Homework Statement

T: R2-->R2 first reflects points through -3pi/4 radian (clockwise) and then reflects points through the horizontal x1-axis. [Hint T(e1)= (-1/sqrt2, 1/sqrt2)

The Attempt at a Solution

I just don't understand why the points would be (-1/sqrt2, 1/sqrt2). If it's -3pi/4, why wouldn't it be (-(sqrt2)/2, -(sqrt2)/2)?

 

[HallsofIvy]

Did you miss the part about the reflection or are you rotating the wrong way? Rotating (1, 0) -3pi/4 radians (clockwise as it says) gives you (-1/sqrt(2), -1/sqrt(2)) but then the reflection through the horizontal axis changes that to (-1/sqrt(2),+1/sqrt(2)).

 

[fk378]

Doesn't -3pi/4 radians correlate to (-(sqrt2)/2, -(sqrt2)/2) though (on a unit circle)? Where is the sqrt2 on the bottom coming from?

 

[HallsofIvy]

Are you aware that 2= (sqrt(2))*(sqrt(2))? 1/sqrt(2) is exactly the same as sqrt(2)/2.