3. A ball is thrown with an initial velocity of 70 ft/sec, at an angle of 35° with the horizontal. Find the vertical and horizontal components of the velocity.

Let the transformation T : IR³ →R² be given by the formula T(x,,X2,X3) = (2x, –x,, X, +3x;). Find the standard matrix of this transformation and write it in matrix multiplication form. Check correctness of your answer for the point (1,4,-3).

A spy stands on the sidewalk by an apartment building examining a foreign embassy across the street. The spy then climbs 30 m to the top the building and then slides 40 m along a wire at a 20° angle below horizontal to reach a window on the embassy. What is their total displacement from the sidewalk to the embassy window?

A projectile was fired from level ground and just cleared a wall that is 10 m high and 20 m from the point of projection. If the angle of projection was 36°, find the initial speed of the projectile in m/s correct to the nearest integer.

Could you explain how to show this in detail?