Use the matrices P and D to construct a spectral decomposition of A PDP 18 3 8 -24 4 18 3 0 0 13 -4 2 8 18 3 A spectral decomposition of A is A uuu2u here u, u2ua Simplify your answers.)

Atoy company is considering a cube or sphere-shaped container for packaging a new product. the height of the cube would equal the diameter of the sphere . compare the volume to surface area ratios of the containers. which packaging will be more efficient? for a sphere, sa =4πr²

An automated water dispenser fills packets with one liter of water on average, with a standard deviation of 5 milliliter. the manual says that after a year of operation the dispenser should be tested to see if it needs recalibration. a year later a number of filled packets are set aside and measured separately. it is found that the average packet now contains about 0.995 liters. does the dispenser need calibration? explain your answer.

What is the absolute value of the complex number -4-sqrt2i