ENT 300 exam I redo

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lacythecoolest
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312292
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ENT 300 exam I redo
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2015-11-30 20:47:50
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engineering
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redo of exam I quiz
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  1. Engineering technology students know that Euler's identity (e^(i*pi)+1=0) is easy to understand, because e^(i*pi) is a complex number in polar form and is equal to -1.
    true
  2. Some say that Euler's identity (e^(i*pi)+1=0) is so mysterious that it can hardly be comprehended.
    true
  3. Some say that Euler's identity (e^(i*pi)+1=0) is so mysterious that it can hardly be comprehended.
    true
  4. AC voltage of 5*exp(0.927i) has an phase of
    0.927 radians
  5. AC voltage of 5*exp(i53.13 deg) has an amplitude of
    5 volts
  6. sin(z), cos(z), tan(z), ln(z), log(z) are defined when z is a complex number
    true
  7. exp(i*z) is the same as
    cos(z)+i*sin(z), which is know as Euler's formula
  8. Complex numbers can be

    A) added and subtracted
    B) multiplied and divided
    C) placed in matrices
    D) all of these
    D) all of these
    (this multiple choice question has been scrambled)
  9. The sum of 3 and i4 has an angle of

    A) 0.927 radians
    B) both of these
    C) both of these
    D) 53.13 degrees
    B) both of these
    (this multiple choice question has been scrambled)
  10. The sum of 3 and 4i is
    exp(0.927i)*5
    5*exp(0.927i)
    both of these
    • exp(0.927i)*5
    • 5*exp(0.927i)
    • both of these
  11. exp(-i*pi/2)*3=e^(-i*pi/2)*3 is a complex number in polar form and is also
    3
    -3i
    3i
    -3
    -3i
  12. exp(-i*pi)*2=e^(-i*pi)*2 is a complex number in polar form and is also
     2i
    2
    -2
    -2i
    -2
  13. exp(i*pi)*1=e^(i*pi)*1 is a complex number in polar form and is the same as
    1
    -1
    -i 
    i
    -1
  14. exp(1)=e^(1) is known as Euler's number and is
    2.71828
  15. The angle (radians) of the sum of 3 and i4 is

    3+i4
    7
    5
    0.9273
    0.9273
  16. The magnitude of the sum of 3 and i4 is
    7
    5
    3+i4
    sqrt(3^2+(4i)^2)
    5
  17. The sum of 3 and 4i is
     5
    3+i4
    sqrt(3^2+4^2)
    7
    3+i4
  18. The angle of 3+i4 is
    53.13 deg
    3
    5
    4
    53.13 deg
  19. The magnitude of 3+i4 is
    53.13 deg
    3
    5
    4
    5
  20. The imaginary part of 3+4i is
    53.13 deg
    5
    3
    4
    4
  21. The real part of 3+i4 is
    3
    5
    i4
    4
    3
  22. The number (3+i4) is an example of a _______ number in rectangular form.
    imaginary
    complex
    real
    polar
    complex
  23. Complex numbers
    are frequently used in electrical engineering
  24. A complex number is
    like a 2D vector
  25. i^4 is
    -1
    1
    -i 
    i
    1
  26. i^3 is
    i
    -i
    1
    -1
    -i
  27. i*i is
    j
    -1
    i
    1
    -1
  28. The square root of -1 is
    the symbol i (usually and in calculators) or the symbol j (in electrical engineering)
  29. The augment function in the TI-89
    combines two vectors into a matrix
  30. x/norm(x) sto--> uu(x) is a TI-89 function. Then typing: uu(A) will calculate the ______ of vector-A
    unit vector in the direction
  31. In calculating torque-T about point-O by T=crossP(R,F), the direction of T
    perpendicular to both R and F and is given by the right-hand rule
  32. In calculating torque about point-O by crossP(R,F), R
    vector from point-O to any point on the line of action of force-F
  33. The formula for calculating torque is
    R cross F = crossP(R,F)
  34. acos( dotP(a,b) / ( norm(a) * norm(b) ) ) sto-> nn(a,b) is a TI-89 function that computes the
    angle between vectors a and b
  35. In crossP(a,b) = c
    c is perpendicular to both a and b
  36. Regarding a,b,c in crossP(a,b) = c,
    all are 3D vectors
  37. The cross-product operation is commutative which means crossP(a,b) = crossP(b,a)
    false
  38. The dot-product operation is commutative which means dotP(a,b) = dotP(b,a)
    true
  39. . A 3D vector with components a,b, and c can stored into a column vector as
    [a;b;c]
  40. A 3D vector with components a,b, and c can be stored into a row vector as
    [a,b,c]
  41. The cross product of two 3D vectors is useful
    in 3D torque problems
  42. The cross product of two 3D vectors is
    a 3D vector
  43. The magnitude of the cross product of two vectors A and B is
    norm(A)*norm(B)*sin(theta)
  44. The length of a 3D vector A=[a,b,c] is norm(A)=
    sqrt(a*a + b*b + c*c)
  45. The dot product of two vectors A and B is defined as dotP(A,B)=
    norm(A) * norm(B) * cos(theta)
  46. The dot product is useful for calculating the angle between two vectors:
    (2D or 3D)
  47. The dot product of two 3D vectors is
    a scalar (not a vector), which is the same as a number
  48. vector = [1.2, 3.4, 5.6], where 1.2 is called the _____ component
    first
  49. A vector that has a length of one is called a ______ vector.
    unit
  50. In the TI-89, the magnitude of _______ can be determined by the _____ function.
    a 2D or 3D mechanical vector, norm()
  51. Orthogonal means
    perpendicular to
  52. Dot products and cross products are not defined for
    complex numbers
  53. Dot products are great for finding
    angle between two vectors in 2D or 3D.
  54. Dot products are defined for
    mechanical vectors, but not for complex numbers
  55. A vector with a magnitude of one is called ______ vector.
    a unit
  56. . When a vector is multiplied by a scalar, the scalar is multiplied by
    each vector component or the vector magnitude
  57. A complex number that has an angle of zero is called
    a scalar
  58. Mechanical vectors and complex numbers can be added and subtracted
    true
  59. A complex number of magnitude 5 and angle 53.13 degrees
    (3+3i)
    (3+4i)
    (4+4i)
    (4+3i)
    (3+4i)
  60. In the TI-89, the complex number with an x-component of 3 and y-component of 4 is ______, where "/_" is the "angle" symbol, common in the TI-89.
    (5 /_ 53.13 deg )
    [5 + /_ 53.13 deg ]
    (5 + /_ 53.13 deg )
    5 /_ 53.13 deg
    (5 /_ 53.13 deg )
  61. In the TI-89, the complex number with an x-component of 2 and y-component of 3
    [2+3]
    [2,3]
    (2,3i)
    (2+3i)
    (2+3i)
  62. In the TI-89, the mechanical vector with an x-component of 2 and y-component of 3
    (2+3i)
    [2+3]
    (2,3i)
    [2,3]
    [2,3]
  63. TI-89 modes: radian and either rectangular or polar. Enter the complex number in polar form. "/_" is the angle symbol. The complex number is equivalent to (3+4i) = (5/_53.13 deg)
    d= (5*e^(53.13*i))
    b= ( 5*e^(i*53.13*pi/180) ) a= (5 /_ (53.13*pi/180) )
    c= (5 /_ 53.13)
    either a or b but not c or d
    either a or b but not c or d
  64. In the TI-89, mechanical vectors are placed in ____ separated by commas.
    brackets
  65. Given x and y components of a vector in the first quadrant, the angle is
    atan(y/x)
  66. Given x and y components of a vector in the first quadrant, the magnitude is
    sqrt( x^2 + y^2)
  67. Given a vector (M-angle-theta)=(M/_theta), where theta is in the first quadrant, the vertical component is
    M*sin(theta)
  68. Given a vector (M-angle-theta) in the first quadrant, the horizontal component is
    M*cos(theta)
  69. The manual way to add two vectors is to
    add horizontal components and add vertical components
  70. Two vectors are added by placing the tail of the
    second vector at the head of the first vector.
  71. Length of a vector and direction of a vector are identified as
    magnitude and angle
  72. . i in a complex number identifies the _____ of the complex number.
    vertical component
  73. Complex numbers are the same as 2D _____ vectors
    mechanical
  74. A complex number (electrical vector) can be resolved into horizontal and vertical components called
    real and imaginary parts
  75. A mechanical vector can be resolved into horizontal and vertical parts called
    x and y components
  76. A vector has
    magnitude and direction
  77. TI-89 angles are measured
    positive when counterclockwise from x-axis
  78. Airplane angles are
    always positive
  79. An airplane angle of ____ is the same as 100 degrees.
    N10W or 10 degrees NW
  80. Airplane angles are measured from
    North or South
  81. The maximum airplane angle is _____ degrees
    90
  82. A vector with an angle of negative-pi/2 radians point along the _____ axis
    -y
  83. A vector with an angle of negative-pi radians point along the _____ axis
    -x
  84. A vector with an angle of pi radians point along the _____ axis
    -x
  85. A vector with an angle of pi/2 radians point along the _____ axis
    +y
  86. Positive angles "go" _______ from the ________.
    counterclockwise, x-axis
  87. Angles are measured relative to the
    positive x axis
  88. The number of gradians in 360 degrees is
    400
  89. The dimension of a radian is
    dimensionless - a radian has no dimensions
  90. An angle of one radian occurs when the _____ and the arc length are ____.
    radius, the same
  91. The angle measured in radians is
    the arc length divided by the radius
  92. The number of degrees in one radian is approximately
    57
  93. The number of radians in 180 degrees is
    pi
  94. The matrix method in solving simulaneously linear equations is most efficient because
    the unknown variables, x and y, are not entered into the calculator

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