For a finite rotation by an angle \alpha about the z axis, apply the rotation operator u_r to the function f(r)=ax+by and show that it transforms correctly.

How many square feet of out door carpet will we need for this hole? 8ft 3ft 12ft 4ft

Abby is preparing fruit punch for her party. she starts with a bowl filled with liquid that has 1/2 fruit juice and 1/2 sprite, but she decides it's too fruity. so she pours out 1/4 of the liquid, and then fills the bowl up again with sprite. what fraction of the punch is now sprite?

It took alice 5 5/6 hours to drive to her grandparents' house for . on the way home, she ran into traffic and it took her 7 3/8 hours. how much longer did the return trip take? write your answer as a proper fraction or mixed number in simplest form. the trip home took __hours longer. ?