Matrix A is singular if the determinant of A is 0. For what value(s) of z is matrix A singular?

What is the value for A₁₂?

The position vectors of the points A and B, relative to an origin O, are given by:

What is the magnitude of the vector ?

Two vectors are described by the following equations, where i and j are unit vectors in the x- and y-directions:

a = 2i + j

b = i + 3j

What is the angle between these two vectors? Give your answer in degrees (round to whole integer).

Calculate the angle (in degree) between the vectors a and b, where i, j and k are unit vectors in the x-, y- and z-directions

a = 2i + 3j - k

b = -4i + j + 5k

Give your answer to 2 decimal places.

Solve the following definite integral:

What will the gradient of the following function be when x = 2?

What does differentiation represent (select all that apply)?

How do you find the area under a curve in a graph?

What is 0.25 radians in degrees?

Give your answer to 2 decimal places.