# linear

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**Problem xxx**a)

xxx xxxxxx xxx xxxxxxxx xxx counterclockwise xxxxxxxx xx xxxxxx xx

The xxxxxx xxx translation by a vector = xx

xx

xxx matrix xxx xxxxxxxxxxx xx x vector x xx

The xxxxxx xxx rotation xxx xxxxxxxxxxxxxxxx xx xxx center xx

c) Let the center xx rotation xx

we xxxx xxxx xxxxx .

xxx xxx fact we xxx find xxxx and x Hence, is x counterclockwise xxxxxxxx by 90o at xxx xxxxxx x

**xxxxxxx xx**

The xxxxx xxxxxx xxxx xxxxxxxxx xx x

Since xx x xxxxxxxxx rotation xxxxxxxx at origin x xxx the angle xx xxxxxxxx equals to the acute xxxxx xx the xxxxxxxxxxxxxx xx xxxx x xxx x

xxxxxx

Check the answer:

which matches xxx diagram.

**Problem xx**

xx

xxxxxx xxxxxxx the xxxxxxxx xxxxxxxxxxxx xx a factor of xx xx xxx xx xxxx by using x xxxxx xxxxxx about xxx center xx xxxxxx by xx xxxxxx xxx triangle. xx can xxx xxx matrix .

Then the xxxxxxxxxx xxxxx the line xx

xxxxxxxx xxx xxxxxxxxxxx by vector is

Hence, the xxxxxxxx xxxxxx transformation is

xx Let xx a xxxxx xx the

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