Please solve all problem with as much detail as possible as this will be used as a study guide for my upcoming quiz.

Sample Quiz #2

1) Vectorize each of the following MATLAB expressions:

(a) sqrt(1 ^ 2)q+

(b) 1 / q

2) For

1 0.5

2 3

A

= −

and

2 1

1 0.2

B

= −

, manually, find the determinants of A , B , and C AB= .

3) Write the polynomial 2( ) 2 15f x x x= − − as a product of first order factors.

4) Obtain 3 1 2/c c c= , where 1 2 3c j= + and 2 3c j=− + .

5) For the sinusoidal voltage ( ) 3 cos(20 / 6)x t tπ π= − + mV, find the amplitude, frequency, period

and phase angle. Give units with each answer.

6) Find the phasor X of ( ) 7 sin(4 / 6)x t tπ π= − − .

7) Use 10ω π= rad/sec, and find the sinusoidal time function that has the phasor: X j= − .

8) Use a = -2, b = 3 and c = 5, and find the results of

(a) d = a^2 >= c

(b) e = (a > b -4)+c <= b^2
(c) f = a+b == c-4
9) For a = 2, b = 0 and c = -5, find the results of
(a) d = a | (b & c)
(b) e = and(a,b)|c
(c) f = a & c | ( b & ~a)
(d) g = a & c | b & ~a
(e) h = (b && c) | (b || a)
(f) p = a & xor(~b,c)
10) For a = -2, b = 4 and c = 2, find the results of
(a) d = (a ~= c -2) & a^2 > b,

(b) e = sqrt(a^2 + b^2) < abs(c) | (a+b)/2 >= c ,

ECE 115, Quiz #2, F/12

Name _______________________________ Lab Sect.______ Score______

1) Write the polynomial:

2( ) 2 2f x x x= + + , as a product of first order

factors.

2) Given is: 2 3y j= − − . Give y in polar form.

3) Given are: 1 3c j= − and 2 1 2c j= − − . Find the imaginary part of 3 1 2/c c c= .

4) Given is: ( ) 5sin ( 60 / 3)x t tπ π= − + . Find

(a) the frequency f in Hz of ( )x t

(b) the period 0T in seconds of ( )x t

(c) the amplitude A of ( )x t

(d) the phasor X of ( )x t . Hint: cos( ) cos( ) cos( ) sin( ) sin( )α β α β α β+ = − .

5) The period of the sinusoidal function ( )v t is 0T = 10 m sec , and its phasor is:

2 /35 jV e π= . Give ( )v t .

6) Give a sketch of: ( ) 5sin (10 )x t tπ= over 0 0.4t≤ ≤ . You must label the

vertical and horizontal axes.

7) For 2 , 1a b= = − and 1c = , find

(a) ( 4) ^ 2x a b c b= > − + <= (b) ~ & | ( & ~ )x a c b a= (c) ( ~ 2) | ^ 2x a c a b= = − >