Suppose that H is a subgroup of G and let G act by conjugation on the set X = {gHg-1 : g ∈ G}. Describe, as precisely as possible, the stabilizer of H under this action.

Let H be a subgroup of G of index 2. Prove that H is a normal sub-group of G.

0.5 A rental truck costs $45.45 for a day plus 94¢ per mile. (a) If x is the number of miles driven, write an expression for the total cost C, in dollars, of renting the truck for a day.C =        (b) Find the total cost of the rental if it was driven 188 miles.C = $

Let T : R3 → R² bc given by a +b-2c -36 + c Tb