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.

On the first of each month, shelly runs a 5k race. she keeps track of her times to track her progress. her time in minutes is recorded in the table: jan 40.55 july 35.38 feb 41.51 aug 37.48 mar 42.01 sept 40.87 apr 38.76 oct 48.32 may 36.32 nov 41.59 june 34.28 dec 42.71 determine the difference between the mean of the data, including the outlier and excluding the outlier. round to the hundredths place. 39.98 39.22 0.76 1.21

Ling listed all of the factors of a mystery number: 1,2,4,8,16,32 what is the mystery number?

Solve the system of equations y= 3/2 - 1, -x+ y =-3