Why do we need to have a reference temperature to define thermal coefficient of resistance (TCR)?   TCR is the change in resistance per change in temperature divided by the resistance at a specified, fixed reference temperature:
In my textbook, a relationship is plotted between the resistance of the material and the temperature, and the temperature coefficient is defined as the slope of that graph divided by an arbitrary resistance $R_1$ on the graph. Does that mean that the coefficient varies depending on the temperature I choose to divide the slope by?  If so, how does it stand as a valid reference to the material’s resistance growth rate with temperature?  If not, then where did I go wrong with this train of thought?
Evaluate  $$\int\frac{e^xdx}{(e^{2x}-1)(e^x+1)}$$  I tried to decompose the integrand into A and B partial fractions.  No success. This is something I just realised I don't entirely know the answer to, so I'm going to ask it here as I think it's interesting.  In most non-scientific writing on depth of field, diagrams generally show camera and subjects as being perfectly parallel, e.g.    However, is this a more accurate representation of the focal plane?    Are there ways to optically alter the shape of the focal plane?  Note: Obviously these diagrams are two dimensional, but I'm assuming in the second diagram the shape would be spherical with the sensor at the center. When is the formula $$S_{\infty} = \dfrac{a}{1-r}$$ valid?   Does |$r| &lt;1$? Trigger an event with Prototype I've read that it is possible to add a method to an existing object (i.e., not in the class definition) in Python.   I understand that it's not always good to do so. But how might one do this? Let $\mathbf A, \mathbf B$ be Hermitian matrices of the same size. What is the characterization of $\mathbf A, \mathbf B$ such that $p(\lambda)=\det(\mathbf A-\lambda\mathbf B)=0$ has only real roots?   If $\mathbf B$ is positive definite (I corrected this), it is easy to see $p(\lambda)$ has only real roots. How to execute a script just by double clicking like .EXE files in Windows? Why is it called an “Indian file”? Lightsabers are not made of light, nor have they anything to do with lasers (even if there are people who mistakenly refer to them as "laser swords").   Blaster bolts are also not lasers. They travel significantly slower than light, they travel even slower than ordinary bullets fired by gunpowder. (called slug throwers on the Star Wars universe)  Was there any use of lasers ever presented in the Star Wars universe, either as we use them today, or as weapons?  By laser I mean something which behaves like laser does, even if it's not called by that name in a movie or book. If something is called a laser (in the script or by fans) but clearly doesn't work like a laser (for example, it travels slowly, and in visible blocks) it doesn't count. How do you associate the .exe file extension with a program in Windows? Ball to Ball Collision - Detection and Handling With the help of the Stack Overflow community I've written a pretty basic-but fun physics simulator.    You click and drag the mouse to launch a ball.  It will bounce around and eventually stop on the "floor".  My next big feature I want to add in is ball to ball collision.  The ball's movement is broken up into a x and y speed vector.  I have gravity (small reduction of the y vector each step), I have friction (small reduction of both vectors each collision with a wall). The balls honestly move around in a surprisingly realistic way.  I guess my question has two parts:   What is the best method to detect ball to ball collision? Do I just have an O(n^2) loop that iterates over each ball and checks every other ball to see if it's radius overlaps? What equations do I use to handle the ball to ball collisions? Physics 101 How does it effect the two balls speed x/y vectors?  What is the resulting direction the two balls head off in?  How do I apply this to each ball?     Handling the collision detection of the "walls" and the resulting vector changes were easy but I see more complications with ball-ball collisions.  With walls I simply had to take the negative of the appropriate x or y vector and off it would go in the correct direction.  With balls I don't think it is that way.  Some quick clarifications: for simplicity I'm ok with a perfectly elastic collision for now, also all my balls have the same mass right now, but I might change that in the future.    Edit: Resources I have found useful  2d Ball physics with vectors:  2d Ball collision detection example:     Success!  I have the ball collision detection and response working great!  Relevant code:  Collision Detection:  for (int i = 0; i &lt; ballCount; i++)   {       for (int j = i + 1; j &lt; ballCount; j++)       {           if (balls[i].colliding(balls[j]))           {             balls[i].resolveCollision(balls[j]);         }     } }   This will check for collisions between every ball but skip redundant checks (if you have to check if ball 1 collides with ball 2 then you don't need to check if ball 2 collides with ball 1.  Also, it skips checking for collisions with itself).  Then, in my ball class I have my colliding() and resolveCollision() methods:  public boolean colliding(Ball ball) {     float xd = position.getX() - ball.position.getX();     float yd = position.getY() - ball.position.getY();      float sumRadius = getRadius() + ball.getRadius();     float sqrRadius = sumRadius * sumRadius;      float distSqr = (xd * xd) + (yd * yd);      if (distSqr &lt;= sqrRadius)     {         return true;     }      return false; }  public void resolveCollision(Ball ball) {     // get the mtd     Vector2d delta = (position.subtract(ball.position));     float d = delta.getLength();     // minimum translation distance to push balls apart after intersecting     Vector2d mtd = delta.multiply(((getRadius() + ball.getRadius())-d)/d);        // resolve intersection --     // inverse mass quantities     float im1 = 1 / getMass();      float im2 = 1 / ball.getMass();      // push-pull them apart based off their mass     position = position.add(mtd.multiply(im1 / (im1 + im2)));     ball.position = ball.position.subtract(mtd.multiply(im2 / (im1 + im2)));      // impact speed     Vector2d v = (this.velocity.subtract(ball.velocity));     float vn = v.dot(mtd.normalize());      // sphere intersecting but moving away from each other already     if (vn &gt; 0.0f) return;      // collision impulse     float i = (-(1.0f + Constants.restitution) * vn) / (im1 + im2);     Vector2d impulse = mtd.normalize().multiply(i);      // change in momentum     this.velocity = this.velocity.add(impulse.multiply(im1));     ball.velocity = ball.velocity.subtract(impulse.multiply(im2));  }   Source Code:     If anyone has some suggestions for how to improve this basic physics simulator let me know!  One thing I have yet to add is angular momentum so the balls will roll more realistically.  Any other suggestions?  Leave a comment! I rent a VPS that uses a SSD of 10GB (Debian 7) and I upgraded yesterday to their "second tier" plan that uses a 20GB disk. However, the "one-click-upgrade" process didn't work as I expected and what they did was to move my data to a bigger drive without actually extending the partitions. So now I have 10GB of unallocated space.  I do run around 5 websites on this VPS with mail accounts and all that jazz and I'm very scared to mess up anything so I called their support and they offered to do the job for me for 80 EUR that I find unacceptable since I thought it was included when doing the upgrade. Their older offers from last year used to be just a one click job but the excuse is that "SSD's are different, so it's up to the user".  Anyway, how can I actually do that without screwing things up and is it possible to do that on a "live" system?  I know a couple of commands so here it goes what I could find:  root@vpsxxxxxx:~# df -h Filesystem      Size  Used Avail Use% Mounted on rootfs          9.9G  7.6G  1.8G  81% / udev             10M     0   10M   0% /dev tmpfs           388M  200K  388M   1% /run /dev/vda1       9.9G  7.6G  1.8G  81% / tmpfs           5.0M     0  5.0M   0% /run/lock tmpfs           775M     0  775M   0% /run/shm /dev/vda1       9.9G  7.6G  1.8G  81% /var/www/clients/client2/web2/log /dev/vda1       9.9G  7.6G  1.8G  81% /var/www/clients/client1/web3/log /dev/vda1       9.9G  7.6G  1.8G  81% /var/www/clients/client3/web5/log /dev/vda1       9.9G  7.6G  1.8G  81% /var/www/clients/client5/web7/log /dev/vda1       9.9G  7.6G  1.8G  81% /var/www/clients/client4/web6/log  root@vpsxxxxxx:~# fdisk -l  Disk /dev/vda: 21.5 GB, 21474836480 bytes 4 heads, 32 sectors/track, 327680 cylinders, total 41943040 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x00000000     Device Boot      Start         End      Blocks   Id  System /dev/vda1   *        2048    41943039    20970496   83  Linux  root@vpsxxxxxx:~# sfdisk -l  Disk /dev/vda: 41610 cylinders, 16 heads, 63 sectors/track Warning: The partition table looks like it was made   for C/H/S=*/4/32 (instead of 41610/16/63). For this listing I'll assume that geometry. Units = cylinders of 65536 bytes, blocks of 1024 bytes, counting from 0     Device Boot Start     End   #cyls    #blocks   Id  System /dev/vda1   *     16  327679  327664   20970496   83  Linux /dev/vda2          0       -       0          0    0  Empty /dev/vda3          0       -       0          0    0  Empty /dev/vda4          0       -       0          0    0  Empty General system specs for large scenes in blender What are the system requirements for working with complex geometry in Blender? Things like RAM, GPU, CPU etc.? Let $X, Y$ be an exponentially distributed random variables with parameters $a, b$. Then $X$ has pdf:    $$f_X(x) =\begin{cases} a e^{-a x},&amp; x\geq 0\\ 0,&amp; \text{otherwise}.\end{cases}$$ Suppose $X$ and $Y$ independent. Show that $$\mathbb P(X&gt;Y) = \frac{b}{a+b}.$$   Now I thought the following: $$f(x,y) = f_X(x)\ f_Y(y) = abe^{-ax -by},\qquad\text{for } x,y &gt; 0.$$ And then $$\mathbb P(X&gt;Y) = \int_0^\infty \int_0^x a b e^{-ax -by}\,dydx$$ However, if I solve this (manually or using Wolframalpha), I can't seem to end up with $\frac{b}{a+b}$. Any ideas? Cardinality of cartesian square Given an infinite set $A$ -  does the cardinality of $A$ equal to the cardinality of $A^2$? How to specify that search should be between two dates in technical specification I'm writing an integration manual that specifies how to use our WCF service for mobile messages and responses. The part in question needs to specify that the search results will be filtered between the start and end dates.  My aim is to make it clear that the time portion of the two dates will be discarded and the result will include everything from the start date to the end date. (In practice the code truncates the dates, adds one day to the end date, and returns the data that conforms to a query something like:  SELECT * FROM Table WHERE DateCreated >= @StartDate AND DateCreated &lt; @EndDate)  But my paragraph looks verbose and clumsy. It doesn't feel right. I feel kind of like John Cleese telling the kids when to put their clothes onto a lower peg. How can I make this less verbose?  Or maybe I'm over-thinking this?     When searching for responses, the search is performed between the supplied dates, after truncating the time portion thereof. The results will include responses with a date-time greater than equal to the start date, and less than one day after the end date. So passing the same value for start and end date will retrieve all responses received on that date, for messages previously sent by that user. Calculating peaks in DEM using GRASS What is a word for "cannot-be-wrong" attitude? When speaking with someone recently I was continuously taken aback by how he could not concede even the slightest detail in my argument (which was not unreasonable), and it happened another time previously. Both times had to do with me pointing out 'error' in his action.  He very much exhibits that 'I cannot be wrong' attitude.  I first thought to call this arrogance or pride but he is not overbearing like arrogance demands and he does not show excessive self esteem that pride demands.  What is a word that can accurately describe this attitude? How to quickly move one layer to a different group in large Photoshop files, without dragging? How does the T-1000 see? In Terminator 2: Judgement Day, how does the T-1000 sense things? It's made of mimetic poly alloy; however, does it have a retinal scan camera like the T-X or T-800, or is just molecules that allow it to see what it does? In other words: let's say it is made out of nanobots. Would a group of these nanobots provide the capability of sight? Kind of like humans with cells that  make up the brain? I have always wondered whether James Cameron explained this on a special edition or if the topic was left up for insight from Terminator fans. From what I get from the whole mimetic poly alloy and some of the extra scenes, it seems to feel its way out to get information. Of course, it's very much not blind! Thoughts?