Compute the indicated matrices, if possible .A^2Blet A=begin{bmatrix}1 & 2 3 & 5 end{bmatrix} text{ and } B=begin{bmatrix}2 & 0 & -1 3 & -3 & 4 end{bmatrix}

A radar station, located at the origin of xz plane, as shown in the figure , detects an airplane coming straight at the station from the east. At first observation (point A), the position of the airplane relative to the origin is $\overrightarrow{R_A}$. The position vector $\overrightarrow{R_A}$ has a magnitude of ${\displaystyle {360}^m}$ and is located at exactly ${\displaystyle {40}^{\circ }}$ above the horizon. The airplane is tracked for another ${\displaystyle {123}^{\circ }}$} in the vertical east-west plane for ${\displaystyle {5.0}^s}$, until it has passed directly over the station and reached point B. The position of point B relative to the origin is $\overrightarrow{R_B}$ (the magnitude of $\overrightarrow{R_B}$ is ${\displaystyle {880}^m}$). The contact points are shown in the diagram, where the x axis represents the ground and the positive z direction is upward.

Define the displacement of the airplane while the radar was tracking it: ${\overrightarrow{R}}_{BA}={\overrightarrow{R}}_B-{\overrightarrow{R}}_A$. What are the components of ${\overrightarrow{R}}_{BA}$
Express ${\overrightarrow{R}}_{BA}$ in meters as an ordered pair, separating the x and z components with a comma, to two significant figures.

An extreme skier, starting from rest, coasts down a mountainthat makes an angle ${\displaystyle {25.0}^{\circ }}$ with the horizontal. The coefficient of kinetic friction between her skis and the snow is 0.200. She coasts for a distance of 11.9 m before coming to the edge of a cliff. Without slowing down, she skis offthe cliff and lands down hill at a point whose vertical distance is 4.20 m below the edge. How fast is she going just before she lands?

A 0.145 kg baseball pitched at 39.0 m/s is hit on a horizontal line drive straight back toward the pitcher at 52.0 m/s. If the contact time between bat and ball is ${\displaystyle 1.00\times {10}^{-3}}$ s,calculate the average force between the bat and ball during contest.

A 1.0 kg ball and a 2.0 kg ball are connected by a 1.0-m-long rigid, massless rod. The rod is rotating cw about its center of mass at 20 rpm. What torque will bring the balls to a halt in 5.0 s? Answer in Nm.

The rate of return.
Given information:
$\begin{array}{|cccc|}\hline Year& CashFlow& IRR@39\mathrm{\%}& PresentValue\\ 0& -\$200& 0& -200\\ 1& 350& 0.719& 251.65\\ 2& -100& 0.517& -51.70\\ \hline\end{array}$
As PV at ${\displaystyle 39\mathrm{\%}}$ is zero. So, the rate of return is ${\displaystyle 39\mathrm{\%}}$.
PV Value at ${\displaystyle 39\mathrm{\%}}$ is calculated using the table.

A relief airplane is delivering a food package to a group of people stranded on a very small island. The island is too small for the plane to land on, and the only way to deliver the package is by dropping it. The airplane flies horizontally with constant speed of 220 mph at an altitude of 800 m. The positive x and y directions are defined. For all parts, assume that the "island" refers to the point at a distance D from the point at which the package is released, as shownin the figure. Ignore the height of this point above sea level. Assume that the acceleration due to gravity is g=9.80 .

How many 3d electrons does an ${\displaystyle F{e}^{3+}}$ ion have?