Questions removed...
Thought I was doing a nice thing, but it's not allowed...
dumplinghao123 wrote:1. (This is actually the last question of the test.)
Q: Z17 is the modular 17 ring. Consider the group of all the invertible elements under multiplication. Which of the following is the generator of such group?
I.5
II.8
III.16
A: I thought they all are (at the test). But the correct answer is 5 only. Could refer to this wiki link for generators:
http://en.wikipedia.org/wiki/Multiplica ... s_modulo_n
2. There is a tank with salty water. The total volume is 100 liter, and 3 grams of salt was initially there. Now pour in the water with 0.02 per liter salty water with speed of 4 liters per minute. Assuming the salt and water mix instantly, and also pouring out the water at 4 liters per minute. In 100 minutes, how many grams of salt are there in this tank?
A: Set the function for salt is f(t). df/dt = 0.08-4*f(t)/100.
Solving this ODE by multiplying e^0.04t.
d(e^0.04t*f)=d(2*e^0.04t)
e^0.04t*f=2*e^0.04t+c
f=2+c/e^0.04t
at t=0, f=3, solve for c, get c=1
thus at t=100, f=2+e^0.04t
3.
Q: There is a line in 3-D space with the following expression:
x=5*cos(t)
y=5*sin(t)
z=t
If there is a point from which to (5,0,0) the length is 26. What’s the distance from this point to the origin?
A: dr = sqrt(26)*dt, so solve it, and get t = -sqrt(26), so the point is sqrt(25+26)=sqrt(51).
4.
Asking for a plane that’s orthogonal to both of the planes.
5.
Giving a matrix, asking the orthonormal basis of the column space.
6.
Q: How many spanning trees are there for 5 vertices under to isormorphism?
A: My answer was 3.
I will post more if I could remember...
mindreader wrote:dumplinghao123 wrote:1. (This is actually the last question of the test.)
Q: Z17 is the modular 17 ring. Consider the group of all the invertible elements under multiplication. Which of the following is the generator of such group?
I.5
II.8
III.16
A: I thought they all are (at the test). But the correct answer is 5 only. Could refer to this wiki link for generators:
http://en.wikipedia.org/wiki/Multiplica ... s_modulo_n
2. There is a tank with salty water. The total volume is 100 liter, and 3 grams of salt was initially there. Now pour in the water with 0.02 per liter salty water with speed of 4 liters per minute. Assuming the salt and water mix instantly, and also pouring out the water at 4 liters per minute. In 100 minutes, how many grams of salt are there in this tank?
A: Set the function for salt is f(t). df/dt = 0.08-4*f(t)/100.
Solving this ODE by multiplying e^0.04t.
d(e^0.04t*f)=d(2*e^0.04t)
e^0.04t*f=2*e^0.04t+c
f=2+c/e^0.04t
at t=0, f=3, solve for c, get c=1
thus at t=100, f=2+e^0.04t
3.
Q: There is a line in 3-D space with the following expression:
x=5*cos(t)
y=5*sin(t)
z=t
If there is a point from which to (5,0,0) the length is 26. What’s the distance from this point to the origin?
A: dr = sqrt(26)*dt, so solve it, and get t = -sqrt(26), so the point is sqrt(25+26)=sqrt(51).
4.
Asking for a plane that’s orthogonal to both of the planes.
5.
Giving a matrix, asking the orthonormal basis of the column space.
6.
Q: How many spanning trees are there for 5 vertices under to isormorphism?
A: My answer was 3.
I will post more if I could remember...
Wow, it seems that we did not take the same exam! Are you based in China?
etcetera wrote:Yeah, I instinctively assumed Z17 was of prime order as well.
And I had the same test and am the US.
dumplinghao123 wrote:mindreader wrote:dumplinghao123 wrote:1. (This is actually the last question of the test.)
Q: Z17 is the modular 17 ring. Consider the group of all the invertible elements under multiplication. Which of the following is the generator of such group?
I.5
II.8
III.16
A: I thought they all are (at the test). But the correct answer is 5 only. Could refer to this wiki link for generators:
http://en.wikipedia.org/wiki/Multiplica ... s_modulo_n
2. There is a tank with salty water. The total volume is 100 liter, and 3 grams of salt was initially there. Now pour in the water with 0.02 per liter salty water with speed of 4 liters per minute. Assuming the salt and water mix instantly, and also pouring out the water at 4 liters per minute. In 100 minutes, how many grams of salt are there in this tank?
A: Set the function for salt is f(t). df/dt = 0.08-4*f(t)/100.
Solving this ODE by multiplying e^0.04t.
d(e^0.04t*f)=d(2*e^0.04t)
e^0.04t*f=2*e^0.04t+c
f=2+c/e^0.04t
at t=0, f=3, solve for c, get c=1
thus at t=100, f=2+e^0.04t
3.
Q: There is a line in 3-D space with the following expression:
x=5*cos(t)
y=5*sin(t)
z=t
If there is a point from which to (5,0,0) the length is 26. What’s the distance from this point to the origin?
A: dr = sqrt(26)*dt, so solve it, and get t = -sqrt(26), so the point is sqrt(25+26)=sqrt(51).
4.
Asking for a plane that’s orthogonal to both of the planes.
5.
Giving a matrix, asking the orthonormal basis of the column space.
6.
Q: How many spanning trees are there for 5 vertices under to isormorphism?
A: My answer was 3.
I will post more if I could remember...
Wow, it seems that we did not take the same exam! Are you based in China?
No, I am in US. What you got? How was your questions, are they difficult?
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