(kind of sad the last time I posted here was ages ago and still in this same discussion)
I don't think it needs to be such a long check list. What *most* guys want, nerdy or otherwise, is pretty simple:
-Beauty
-Brains
-Great sense of humour/ability to make fun of themselves
(the order...
Look at this site: http://www.analyzemath.com/Tutorial-System-Equations/determinants.html for references to help
And you can confirm your answers here: http://www.bluebit.gr/matrix-calculator/
Calculating the determinant for A, a 3x3 matrix with elements:
a b c
d e f
g h i
Det(A) = a(ei - fh) - b(di - fg) + c(dh-eg), by starting with row 1.
So -15 is the answer you should be getting.
Use energy conservation + conservation of momentum. You know that since the sliding block isn't losing energy to friction, that all it's energy must be in the form of kinetic and potential energy. At the point it's released, all of it's energy is in the form of gravitational potential energy...
Just look at this picture and you should be able to see how to answer your questions, if you are at all familar with the normal distribution (which your question seems to be about).
http://upload.wikimedia.org/wikipedia/commons/8/8c/Standard_deviation_diagram.svg
It's important to remember how the cross-product is defined before you look at this problem. The cross-product is an operation in a 3-D vector space that produces a third vector.
In this case:
(-1, 2, 0) \times (4, 2, 0) = (0, 0, -10)
The cross product also gives you:
a \times b =...
You can work on research for free, and if it's good, sense it to an academic (professor, pdf) that you respect and trust and they can help you get published.
Do you mean degrees, by certificates? Yes, in the academic community, having a PhD or a DPh is going to make you much more respected than someone with only a BSc. That being said, having reputable publications is also important if you want to be respected.
I'd consider using conservation of energy.
At the point he grabs the rope, he has all kinetic energy and no potential energy. By the time the rope reaches its maximum height, it has no kinetic energy and all potential energy.
It's at least a mental starting point for you to try, as long as...