Curl and divergence
Intuitive analysis of gradient, divergence, curl
Completely clear all output from a Terminal window Where is the "Add vector layer"-button in GRASS 6.4.4. plug-in QGIS 2.10.1? I've just downloaded and installed the new version of QGIS 2.10.1 with GRASS 6.4.4.  When opening a new GRASS mapset and importing layers, I missed the button "Add a new vector layer". I've updated the GRASS plugin, but again the button wasn't there (all other GRASS symbols except "add raster layer" were visuable).  It's maybe a stupid question of a GIS beginner, but what can I Do? Is there an option to add (not import) a vector layer via the GRASS toolbox? Why is the edit button disabled? I was given this question by a friend and after working tirelessly on it I have not come up with anything substantial. I was hoping someone in the community could provide a pointer or possibly a solution. The person who gave me the question says he has the answer to it, but I am more curious about the working.  Here is the question:     Three points $(B, C, D)$ lie on parabola  $y = x^2$ and a fourth point $A$ is placed such that $ABCD$ forms a square. Find the minimal area of $ABCD$.   So far my working out has involved a collection of distance/mid-point formula's and I haven't even reached the point where I differentiate to minimize the area.  Any pointers would be welcome.   Edit  Apparently the correct answer is $\sqrt{2}$ units squared. Why am I asked for a credit card number to download a free app? I  want to download free app in my iPod touch device and i have the following doubts.  Kindly resolve me doubts.   when i try to download it asks my credit card security number. since i am trying to download free app , why do i need to provide my credit card security code? Will i be debited for downloading the free app from app store?   I cant able to find any information regarding this on apple.  Please provide me some references about this from apple and please resolve my doubts.  Thanks a lot. Let $A$ be a diagonalizable matrix and $\lambda$ be an eigenvalue of A. Prove that rank($\lambda I - A$) = rank(($\lambda I - A)^2$). Watermark TextBox in WinForms To power my microcontroller (ATmega8), I am using a ~5.4V voltage source. I want to ensure that I don't accidentally connect the voltage source in reverse, and figured a diode would be a nice way to accomplish this as from what I have learned so far, a diode allows current to flow in one direction, and blocks it in the other.  But what I also learned is that diodes create drops in voltage. I have a few of the typical diodes (1N4001, 1N4148, etc.), and would like to use them to achieve the aforementioned result without dropping the voltage as it would be too low to power the IC.  My question is, is there any way to do this with a diode? Or do I need some other component (if so, what would you recommend)? Show that f(x) = inf{g(x1)+h(x2)} is convex subject to x1+x2=x and where g(.) and h(.) are convex functions.  Can I just go about this by using the regular definition of a convex function or which properties should I use? I know that the sum of convex functions is convex, but the infimum part confuses me. Thank you "Images with street signs" CAPTCHA impossible to solve I just got challenged (over on ) by the new "Mark all images with street signs" CAPTCHA.  I must have tried a dozen times to solve it by checking all images that had street signs, but I never succeeded.  Of note is a text input field without instructions of what to enter there. I suspect that is the problem: It is expecting input, but doesn't tell me what to input.  It's either broken or I am missing something.  I am using Chrome on an iPhone in "full site" mode. Imagine a battery with the positive terminal connected to ground.  The positive side has a high eletrical potential, ground obviously has a lower electric potential.  Electricity wants to seek a lower potential, and there's no significant resistance between the terminal and the ground.  Shouldn't electricity flow?  I know it doesn't but I don't understand why.  I know you have to close the loop, but why is this necessary? Getting Joker from the existing groups in Rummikub I have a group of tiles made up of 3 fours and a joker:     4 4 4 Joker   Now, if a player removes the joker, do they have to replace it with another 4? Is this an instance of Priori Incantatem? During the climax of Fantastic Beasts and Where to Find Them, Tina briefly duels with Graves and their wands appear to lock with each other (see picture). I believe this also happens some other times in the later Harry Potter films other than Harry and Voldemort's duel in the graveyard during Goblet of Fire.    We know that this is definitely a case of Priori Incantatem for the graveyard duel in Goblet of Fire, as the wands are locked for a sufficient amount of time for past spells to begin showing themselves (significantly, showing the people Voldemort had murdered), but is this the case for the other instances of wands locking? If so, does that mean there are a lot more wands out there with shared cores, as it was my understanding this could only happen if that criteria was satisfied? I had Windows 8 installed on my system, which I screwed up, and now I run Ubuntu 12.04. While installing, Ubuntu used all the 461 GB of HDD space (one partition).   Now I want to make a new partition of maybe 100 GB or so, in order to install Windows 7 alongside Ubuntu (with a dual-boot). But I can't even get a partition done. I can't change the partition in GParted either - the option is disabled. Let $\times$ = cross product and $a$ and $b$ have vector signs on them.  $a = [a_1, a_2, a_3]$  $b = [b_1, b_2, b_3]$  How would I prove this? Do I expand out cross product?  Any help is appreciated! When does $\lim_{n\rightarrow \infty} a_n = 0$ imply $\sum_{n = 0}^{\infty} a_n$ converges? This is just a general question. I know the opposite statement is always true. I'm just asking when the converse holds. I know that the converse is not true in some cases, such as for harmonic series. What additional restrictions are needed to make this statement true? When to use ''[verb] that'' I would like to know when to say think(s) that, say(s) that and mean(s) that and when to omit that. A pitcher contains $X + 1$ blue balls and $Y + 1$ red balls. It is known that $X, Y$ are independent random variables, and it is given that $X \sim \mathrm{Poisson}(n), Y \sim\mathrm{Poisson}(2n)$. Calculate the limit: $\displaystyle\lim_{n\to \infty}\mathbb P (X + n = Y) $   I tried to condition on the value of $Y$ and to use the Law of total probability but it did not lead to a solution. ( I tried to sum: $ \sum_{i=0}^\infty\mathbb P(X+n=Y|Y=i)\mathbb P(Y=i) $ and get an expression that I can calculate its limit as n goes to infinity) I installed Oneiric as a guest OS in VirtualBox using the Mini CD. I installed the ubuntu-desktop package and everything seems to work fine - well, except for a font issue with the terminal:    As you can see, some of the letters overlap and it's difficult to read. I checked the settings and it the checkbox "Use the system fixed width font" is checked with "Monospace | 12" selected underneath it.    Edit: running the commands mentioned in the comments:  $ fc-match "Monospace" DejaVuSansMono.ttf: "DejaVu Sans Mono" "Book" $ gconftool --get /desktop/gnome/interface/monospace_font_name Monospace 10 $ debsums ttf-dejavu-core /usr/share/doc/ttf-dejavu-core/AUTHORS                                        OK /usr/share/doc/ttf-dejavu-core/BUGS                                           OK /usr/share/doc/ttf-dejavu-core/NEWS.gz                                        OK /usr/share/doc/ttf-dejavu-core/README                                         OK /usr/share/doc/ttf-dejavu-core/changelog.Debian.gz                            OK /usr/share/doc/ttf-dejavu-core/copyright                                      OK /usr/share/doc/ttf-dejavu-core/langcover.txt.gz                               OK /usr/share/doc/ttf-dejavu-core/status.txt.gz                                  OK /usr/share/doc/ttf-dejavu-core/unicover.txt.gz                                OK /usr/share/fonts/truetype/ttf-dejavu/DejaVuSans-Bold.ttf                      OK /usr/share/fonts/truetype/ttf-dejavu/DejaVuSans.ttf                           OK /usr/share/fonts/truetype/ttf-dejavu/DejaVuSansMono-Bold.ttf                  OK /usr/share/fonts/truetype/ttf-dejavu/DejaVuSansMono.ttf                       OK /usr/share/fonts/truetype/ttf-dejavu/DejaVuSerif-Bold.ttf                     OK /usr/share/fonts/truetype/ttf-dejavu/DejaVuSerif.ttf                          OK Rolling back a completely changed question was originally asked August 9, and received answers. A month later, the OP  the question, invalidating the existing answers. I rolled it back, and left a comment to say that a new question should be opened, but the OP changed it back saying "There is no rule about it, so you can't edit my post."  There is also a bounty on this question, making things more interesting.  What are the guidelines on completely changing a question or rolling back changed questions? Was I out-of-line rolling back the question?  I have no desire to get into an edit war, so I'm not going to touch the question again. If a moderator wants to get involved, great.