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A 10-kg projectile is fired vertically upward from the ground, with an initial velocity of 50 m/s, Fig. 13-7a. Determine the maximum height to which it will travel if (a) atmospheric resistance is neglected; and (b) atmospheric resistance is measured as Fo=(0.01v) N, where v is the speed of the projectile at any instant, measured in m/s.
If resources were abundant, there will be no need to study economics. Discuss
Let X follows a normal distribution with mean 40 and variance 9. Then mean of Y= (X-40)/3 is
Compare and contrast South African government expenditure trends with other global economies
over the past 10 – 15 years
[ 1 0 -1
3. Consider the matrix A = 0 3 0
-1 0 1 ]
- Find the eigenvalues of A.
- Find the eigenspaces corresponding to each eigenvalue from A.
2. Consider a linear transformation T: R3 → R3 defined by
([x [ x + 4y +3z
T y = -5y - 4z
z]) 5x + 10y + 7z ]
Note: T is a 3x1 matrix containing x, y, z respectively. T is equal to another matrix as shown above.
a) Find the matrix A for T
b) Find a basis for ker(T) and the dim(ker(T)). Then find dim(Im(T)), without finding a basis for Im(T). (Show all working)
c) Find a basis for Im(T)
- Answer the following questions
→ → → [ 1
a) Consider the linear transformation T(x) = proju(x), where u = 0
3 ]
Find the matrix for T.
b) Find the matrix for the linear transformation which reflects every vector in R2 across the x-axis and then rotates every vector through an angle of 𝝅/6. (Show all working)
EXERCISE 2: Find the rank and the nullity of the linear transformation S: p_1→ℝ given by
S(p(x)) = ∫_0^1p(x)dx.
If Gouda cheese and cheddar cheese are substitutes, then which of the following would increase the demand for cheddar cheese?
Write a c++ program using function that take an array of integers as input and return the
sum of number in the array.
