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Quiz

Lesson 1 Quiz: Complex Numbers in Trigonometric and Exponential Form and De Moivres Theorem

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  • Questions count: 20
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1.
STEM Integration Problem 20: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
4
6
2
0
2.
STEM Integration Problem 34: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
4
6
0
2
3.
STEM Integration Problem 29: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
2
0
4
6
4.
STEM Integration Problem 12: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
2
0
4
6
5.
STEM Integration Problem 15: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
2
4
0
6
6.
STEM Integration Problem 42: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
0
6
2
4
7.
STEM Integration Problem 6: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
2
0
6
4
8.
STEM Integration Problem 38: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
4
6
0
2
9.
If two vectors \(\vec{A} = (2, k, -3)\) and \(\vec{B} = (4, 2, 6)\) are perpendicular, then the value of \(k\) is:
A) 5
B) -5
C) 10
D) -10
10.
STEM Integration Problem 31: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
4
0
6
2
11.
The evaluation of the definite integral \(\int_{-\pi/2}^{\pi/2} x^5 \cos x\, dx\) is equal to:
C) Zero
D) $2pi$
A) \(pi^5 / 5\)
B) 1
12.
STEM Integration Problem 2: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
2
0
4
6
13.
STEM Integration Problem 21: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
0
6
4
2
14.
STEM Integration Problem 18: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
4
2
6
0
15.
STEM Integration Problem 3: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
4
6
2
0
16.
STEM Integration Problem 37: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
2
6
0
4
17.
STEM Integration Problem 27: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
4
6
2
0
18.
STEM Integration Problem 43: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
4
6
0
2
19.
What is the rigorous mathematical principle for: Equilibrium of a Rigid Body in Classical Statics?
Static equilibrium requires only that horizontal forces balance out (Σ F_x = 0)
Moment of a force is a scalar quantity independent of perpendicular distance
A body is in equilibrium if it rotates with constant angular acceleration
A rigid body is in complete static equilibrium if and only if both resultant force vector equals zero (Σ F = 0) and total algebraic moment about any point equals zero (Σ M = 0)
20.
STEM Integration Problem 25: Evaluate the definite integral ∫[0 to 2] (3x2 - 4x + 1) dx.
6
2
4
0
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