I'm having a very hard time understanding the concept of a "Normal Force." The only framework with which I've come to terms with is imagining the Normal Force as the force exerted when object A comes into contact with object B which keeps object B from losing its macroscopic structural...
Today I was presented with dispersion in my introductory physics class. Before this topic was presented we were told of two important rules for waves: 1) The speed of a wave is dependent on the medium in which it travels and 2) the frequency of wave does not change when going from one medium to...
1. Say that an electron is heading towards the Earth from the sun with an initial known velocity v. And we know that at Earth's surface the magnetic field is given by B1. This B varies as (R1/R2)^2 where R1 is the radius of the earth. How can I find the location in space, R3/R1, where R3 is the...
1. I understand that in order for a force to qualify as doing work it must displace an object. The magnetic field does indeed induce a "force" on a moving charge and displaces the moving charge toward a different trajectory. However, it does not change the kinetic energy of the moving charge. So...
I understand the concept. But do you think there is an algorithm to compute these numbers? Or should I just find the kernel by sticking with row reduction?
My linear algebra uses "Kyle Numbers" to compute some kernels. But it does not elaborate on what they are and how they are used to compute the kernel? Please help.
So I recently came across this video in youtube: . The vibrations of the string definitely look like sinusoidal waves to me and I know that if a string is fixed at both ends then it will display the pattern of nodes and antinodes by producing a standing wave at certain frequencies. Is this how...
1. Find A, a 2x2 matrix, where A^{1001}=I_{2}2. I know that that if A^{2}=I_{2}, then A is either a reflection or a rotation by π.
3. If I use advantage of that fact that A in A^{2}=I_{2} is a rotation by π then I know that A^{1001}=I_{2} is true when A is a rotation by 2π/1001
Is there...
Sorry about the formatting. I'll keep that in mind the next time I post. However, I did not leave out any parts of the problem. The problem simply asked which of these transformations are linear and then provided the 3 equations given.
$$y_{1}=2x_{2}$$
$$y_{2}=x_{2}+2$$
$$y_{3}=2x_{2}$$
I know that in order for a transformation to be linear it has to satisfy:
I) $$T(v + w) = T(v) + T(w)$$
II) $$T(kv) = kT(v)$$
But what are v and w in this case?
note: v and w are vectors and are suppose to have arrows on top of them but I...
I believe this definition should hold true for any vectors as long as they're both in $$ℝ^n$$. You cannot however take the dot product of two vectors if one is in $$ℝ^n$$ and the other is in $$ℝ^m$$ where $$n≠m$$.
I'm having a hard time grasping the concept of a vector geometrically. A vector in $$ℝ^2$$ is a line going in the direction specified from the terms. A vector in $$ℝ^3$$ is similary just a line going in the direction specified by the terms. But what exactly is a vector in $$ℝ^n$$ where n is...
Find the ellipse centered at the origin that runs through
the points (1,2), (2,2), and (3, I). Write your equation
in the form $$ ax^2 + bxy + cy^2 = 1 $$
I understand the $$ ax^2 $$ and $$ cy^2 $$ in the equation because the equation of an ellipse centered at origin is $$ (x/a)^2 + (y/b)^2 = 1...
There was not much additional information which would have helped me arrive at a solution. What would I do after taking the second derivative of x with respect to t? Plug it into equation 1? But then How would I solve my equations then?
So we are given two equations:
$$ \ddot{x} - \dot{x} - x = cost (t) $$
and
$$ x(t) = a sin(t) + b cos(t) $$
The question asks to find a and b.
How would one go about doing this? I thought maybe substituting the $$ cos(t) $$ from equation 1 into equation 2 would work but then what...