D. rates of soil erosion are much lower during droughts that last several years
Answer:
A 1.0 min
Explanation:
The half-life of a radioisotope is defined as the time it takes for the mass of the isotope to halve compared to the initial value.
From the graph in the problem, we see that the initial mass of the isotope at time t=0 is
The half-life of the isotope is the time it takes for half the mass of the sample to decay, so it is the time t at which the mass will be halved:
We see that this occurs at t = 1.0 min, so the half-life of the isotope is exactly 1.0 min.
Answers:
a) 
b) 
Explanation:
a) The centripetal acceleration 
of an object moving in a uniform circular motion is given by the following equation:
Where:
is the angular velocity of the ball
is the radius of the circular motion, which is equal to the length of the string
Then:
This is the centripetal acceleration of the ball
b) On the other hand, in this circular motion there is a force (centripetal force 
) that is directed towards the center and is equal to the tension (
) in the string:
Where 
is the mass of the ball
Hence:
This is the tension in the string
Remember that like charges repel each other. That is, positive repels positive and negative repels negative. Similar to how the north poles of magnets repel each other and south poles repel. However, at the atomic scale, protons, which have positive charge, are more influenced by the "Strong Force," which binds them close together. If they were to be separated ever so slightly, then the electromagnetic force would take over and they would repel each other like you'd expect.
Neutrons are also held together via the Strong Force, but don't have a charge so when separated, don't have an electromagnetic force pushing them away from each other.
However, electrons act differently. There is no "Strong Force" just the electromagnetic force. So, they keep a great distance from each other.
So in an atom, protons and neutrons stay close to each other, taking up little volume, while electrons take up a lot of volume.
BTW, the reason why electrons and protons act differently when they are close together is because protons are made up of smaller particles the carry this Strong Force. For electrons, there is no smaller constituent. And therefore, all you have is the electromagnetic force to influence it. That's it.
Hope that helps.
Answer:
The torque about the origin is 
Explanation:
Torque 
is the cross product between force 
and vector position 
respect a fixed point (in our case the origin):
There are multiple ways to calculate a cross product but we're going to use most common method, finding the determinant of the matrix:
![\overrightarrow{r}\times\overrightarrow{F} =-\left[\begin{array}{ccc} \hat{i} & \hat{j} & \hat{k}\\ F1_{x} & F1_{y} & F1_{z}\\ r_{x} & r_{y} & r_{z}\end{array}\right]](https://tex.z-dn.net/?f=%20%5Coverrightarrow%7Br%7D%5Ctimes%5Coverrightarrow%7BF%7D%20%3D-%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%20%5Chat%7Bi%7D%20%26%20%5Chat%7Bj%7D%20%26%20%5Chat%7Bk%7D%5C%5C%20F1_%7Bx%7D%20%26%20F1_%7By%7D%20%26%20F1_%7Bz%7D%5C%5C%20r_%7Bx%7D%20%26%20r_%7By%7D%20%26%20r_%7Bz%7D%5Cend%7Barray%7D%5Cright%5D%20)
