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While I understand the intuition behind expectation, I don't really understand the meaning of variance and moment.   What is a good way to think of those two terms? How to define a recurrence relation in Maple without the command proc? Give a deduction of $\forall y \exists x (x=y)$  My thinking is I can prove $\exists x(x=y)$ then use generalization theorem， which is equivalent to prove $\neg \forall x \neg (x=y)$ but I got stuck proving this... thanks in advance  Sorry that I did not specify what deduction system that I want to use here, it is the deduction sequence  where ai is either Axiom or original hypothesis or obtained from MP I have a basic grammar question about the past tense. If I met a guy yesterday, which tense should I use about his name today?  For example,     "Yesterday I met a guy, his name is/was John." Determining coordinates of a SHP file i have a SHP file of a building converted from a DXF file. This SHP file is unprojected and have no specific coordinates (origin 0,0). I find WGS84 coordinates (lat, long) of this building from Google Maps. My aim is to replace these coordinates to the SHP file on QGIS.  Could you explain the process step by step?  (I read lots of similar questions, about affine transformation. But i don't know the paramaters.)    What i ask is how to make this transformation in QGIS (step by step)?   SHP file coordinates (not projected)  Scale: 1:142.670.713  X1,Y1: 16.70824, 253.74534  X2,Y2: 1.03521,-6.34918  X3,Y3: 244.00248,-7.49189  Target WGS84 coordinates   X1,Y1: 41.047773, 28.896241  X2,Y2: 41.045452, 28.895929   X3,Y3: 41.045436, 28.899039    I need a second vector layer with coordinates. I have just a SHP file of a building converted from a DXF file. That is not projected. I know where this building is, and can find the WGS84 coordinates from Google Maps. My aim is add WGS84 coordinates to this SHP file and export to replace the building on Google Maps.  My Questions are:  1) I think my SHP file has measurements in meters and unprojected. I have WGS84 lat long coordinates from Google Maps. How can i project this SHP file, for being ready to transformation? Right Click -> Set Layer CRS -> Choose WGS84 EPSG: 4326. Is this enough?  2) qgsAffine plugin just need transformation matrix paramaters. But the answer of @Jochen Schwarze is a bit complex for me. Is there a online calculator? (Just give the source XYs and target XYs and calculate the parameters.)    I think, I have a projection problem before affine transformation. I have a DXF file of a building from AutoCAD. I saved this DXF file as a SHP file in QGIS. But this SHP file is converted from a plain DXF file and is not referenced/projected, it is drawn from coordinates 0,0 in AutoCAD in meters. And the drawing has meters, WGS84 has decimal degrees.  When I set Layer CRS as WGS84 in QGIS, the coordinates don't change.  How can I project this SHP file as WGS84 in QGIS? I'm pretty sure the answer to this should be obvious - even to me ...  It's been a while I've been reading and attempting to construct simple electronic circuits. The supply almost always is either through a battery/cell, or AC duly rectified to DC.   I have the impression electronic circuits rarely ever work off an AC supply.    Is this impression correct? If yes, why is an electronic circuit rarely (if ever) powered/biased using straight AC? My change password interface is not working on java eclipse web application Disabling OBSOLETE error in C# I just read a book "Linear Algebra and Its Applications 4E" by David C. Lay. The book is (should be) LaTeX typeset. The matrix and equations are so nice, please see the following 3 examples:        It's so beautiful, so I want get the same effect inside my paper. Here is my code:   \usepackage{amsmath} \usepackage{colortbl} \newcommand\y{\cellcolor{clight2}} \definecolor{clight2}{RGB}{212, 237, 244}%  %%% \[A=\left[ \begin{array}{ccccc} \y 0 &amp; -3 &amp; -6 &amp; 4 &amp; 9 \\    -1 &amp; \y -2 &amp; -1 &amp; 3 &amp; 1 \\ -2 &amp; -3 &amp; 0 &amp; \y 3 &amp; -1 \\ 1 &amp; 4 &amp; 5 &amp; -9 &amp; -7      \end{array} \right]\]  \[A=\left[\begin{array}{cccccc} \rowcolor{clight2} 3 &amp; -9 &amp; 12 &amp; -9 &amp; 6 &amp; 15\\ 0 &amp; 2 &amp; -4 &amp; 4 &amp; 2 &amp; -6 \\ 0 &amp; 3 &amp; -6 &amp; 6 &amp; 4 &amp; -5 \end{array} \right]\]   And the result:     But how to add these arrows?? Im confused about fire. The way I see it :   Heat creates (kinetic) energy in mass and this creates stronger vibrations of atoms. When those vibrations are strong enough the electrons interact stronger due to electromagnetic forces. This causes the electrons to fly away. This is the creation of a plasma and the direction of most electrons is the direction of the flame. the shape and heat of the flame depends mainly on the amount of electrons and their velocity ( apart from the source of heat and the considered gas and solid material) the electrons move freely ( but not random ) in the flame. there is a chemical reaction going on that usually produces smoke or such. the entropy increases in all the above 6 steps and the process is repeated. the electromagnetic energy is converted into kinetic energy of the electron and conductivity in the plasma (flame). the moving electrons create an electromagnetic field.   That is more or less how I see it. What steps are ok ?  And the main question , why is there light involved ?  I mean why cant we just have kinetic energy of the electrons and a changing magnetic field ? Why are there photons ? If the electrons are in a high energy state why cant they just move faster instead of emitting a photon ???  Why is the light usually visible ? is that because of our structure of air ?  If the light is an electromagnetic wave why does the flame go up ? does that imply all electromagnetic waves go up ?? But electromagnetic waves are not influanced by gravity or buoyancy are they ??  What is the final destiny of the electrons and photons if the heat is gone ??  I am puzzled by this. How to change css property using javascript How to get file creation & modification date/times in Python? Is there a way to use Dvorak keyboard layout, but with command keys mapped to qwerty? I just got off a very long and very frustrating phone call with Apple support.  I purchased a used Apple computer which came installed with Mountain Lion. Meaning that the computer was shipped by Apple with Mountain Lion installed, and received by me with that same installation.  As a precaution, I tried to reinstall Mountain Lion via Recovery mode. This failed because my Apple ID hasn't purchased Mountain Lion.  Apple insisted that because I didn't purchase the computer new, I don't have a license for OS X. I don't believe this is correct, or even legal. This means that anyone using a used computer is doing so illegally, unless they've purchased a separate OS license.  Am I way off-base here? I'm pretty sure I now "own" a copy of Mountain Lion, and Apple is in the wrong. If this is correct, what are my options? Transferring domain to new host, but keeping email on old host I'm helping out a friend manage his website. Said friend has a domain, website.com, which I am transferring from his old host (OLD) to his new host (NEW), but OLD does not provide email services (or, at least, not intuitively). As a result, he wants both:   To host the website at NEW To use the email servers at OLD so he can continue using the email accounts he set up there.   The move from OLD to NEW has taken place, and I have updated the DNS records so they no longer point at ns1.old.com, and now point instead at ns1.new.com, and so on.  But having searched around a bit for the solution to the email aspect, I'm a little uncertain. I've updated the MX record at NEW to point back to ns1.OLD.com, but emails are still failing - and I'm sure the reason for this is obvious, but I'm not quite grasping what I need to do here.  As I understand it, the process ought to be as follows:   Mail sent to account@website.com website.com routes the mail to the host at NEW NEW then uses the new MX record to rout it to the servers at OLD Hey presto, the email should appear in the email inbox at account@website.com at OLD.   But this isn't happening. I get a 550 error telling me to turn on SMTP authentication, which I've read is a sure sign that I've got the MX configuration wrong. Any assistance on this would be really greatly appreciated.  tl;dr: Friend wants to move site hosting to NEW, but keep email hosting at OLD - I don't know what to do with MX and nameservers and so on to make this happen. What are the differences between combat damage, direct damage, and loss of life? SFDC DKIM Setup - Production or Sandbox? Cannot figure out this via SFDC documentation. Need someone who have setup this before to advise.  Basically we want to enable DKIM for our SFDC org. In testing Sandbox and production, the from email address is using the same email domain. For example, "test@abc.com" for sandbox and "contact@abc.com" in production.   Question: shall we setup DKIM in both sandbox and production or just need to setup in production since sandbox and production are actually using the same domain "abc.com"? Google Chrome PPA upgrade invalid signature "Protect Questions" privilege page has confusing wording The wording on the  privilege page is confusing and would benefit from being clarified. See these questions on  and . Suggested wording from  is to replace this:  Which questions can be protected? Any question, even a deleted question, can be protected and unprotected, subject to the following restrictions:  The question must be at least a day old A user can unprotect any protected question   with the following:  Which questions can be protected? Any question at least a day old, even a deleted question, can be protected and unprotected. A user with the privilege can unprotect any protected question. How to succeed with making omelette