Chứng minh rằng một tự đồng cấu f : V → V là đẳng cự khi và chỉ khi nó bảo toàn tích vô hướng, tức là

hf(x)|f(y)i = hx|yi, ∀x, y ∈ V.

Someone this asap for a group of students attends a basketball game. * the group buys x hot dogs at the concession stand for $2 each. * the group buys y drinks at the concession stand for $3 each. the group buys 29 items at the concession stand for a total of $70. how many hot dogs did the group buy?