These problems are on curvilinear one dimensional systems and are giving me a lot of difficulty, if you could provide help along with visuals to help explain that would be very helpful.

1) Which of the following forces is conservative? (a) F = k (x, 2y, 3z) where k is constant. (b) F = k (y, x,
0). (c) F = k (-y, x, 0). For those which are conservative, find the corresponding potential energy U, and
verify by direct differentiation that F = - ∫U.

2) The figure shows a child's toy, which has the shape of a cylinder mounted on top of a hemisphere. The
radius of the hemisphere is R and the CM of the whole toy is at height h above the floor. (a) Write down
the gravitational potential energy when the toy is tipped to an angle from the vertical.(b) For what
values of R and h is the equilibrium = 0 stable?

What pattern would you need to decide that the linear regression model is appropriate? What would you do if you found a curvilinear pattern or no pattern at all? Discuss how to calculate the best-fitting line in a scatter plot (regression analysis).

Using dimensional analysis, which one of the following equations is
(a -> m/^2, v -> m/s, x -> m , t -> s)
a. x = v/t
b. v = 2ax
t2 = x/a
c. x2 = 2av
d. x = at

Describe a method for storing three-dimensional homogeneous arrays. What addressing formula would be used to locate the entry in the ith plane, jth row, and the kth column?

I need help with a simple experiment.
I'm trying to create an experiment that relates to curvilinear motion. However, I'm unsure how to set up an experiment and show all the calculations. Can someone help me with creating a simple experiment to show what curvilinear motion is and do those calculations I can make up the data

One of the problems of storing data in a matrix (a two-dimensional Cartesian structure) is that if not all of the elements are used, there might be quite a waste of space. In order to handle this, we can use a construct called a "sparse matrix", where only the active elements appear. Each such element is accompanied by its two i

Describe the following correlation. The students with the highest grades in written French were also the students with the highest grade in spoken French. The students in the class with the lowest grades in written French also had the lowest grades in spoken French.
Is this:
a) a curvilinear correlation b) no correlation c

Prove that a finite-dimensional extension field K of F is normal if and only if it has this property: Whenever L is an extension field of K and sigma : K ----> L an injective homomorphism such that sigma (c) = c for every c in F, then sigma (K) is contained in K.

1) Show that if dim X = 1 and T belongs to L(X,X), there exists k in K st Tx=kx for all x in X.
2) Let U and V be finite dimensional linear spaces and S belong to L(V,W), T belong to L(U,V). Show that the dimension of the null space of ST is less than or equal to the sum of the dimensions of the null spaces of S and T.
3)

Define two pointers that hold two values of type int. Add these two pointers of type "int" and print the result on the screen.
Define a one dimensional array consisting of five cells, and populate the cells with values 0-5 and then print the result of the one dimensional array on the screen.
Define a two dimensional array