Does multiplying an orthonormal matrix by a vector preserve magnitude.

Multiply. −2x(6x4−7x2+x−5) express the answer in standard form. enter your answer in the box.

Find the value of the variable and the length of each secant segment

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?