Jordan canonical form of 2X2 matrix
For every matrix $A\in M_{2}( \mathbb{C}) $ there's  $X\in M_{2}( \mathbb{C})$ such that $X^2=A$?
What are the differences between git pull and git fetch? What is code coverage and how do YOU measure it? What is code coverage and how do YOU measure it?  I was asked this question regarding our automating testing code coverage. It seems to be that, outside of automated tools, it is more art than science. Are there any real-world examples of how to use code coverage? "Above"/"below" before/after a noun I have seen sentences similar to the following:  (1) See the reference above. (2) See the reference below.  And,  (3) See the above reference.  But not,  (4) See the below reference.  Are all these forms acceptable? Which is/are preferred in formal writing? Evaluate $\sum_{k=1}^\infty\frac{x^k}{k(k+1)}$ My partner is tutoring a Civil Engineering student in maths. Conveniently, I am a civil engineer so when any maths that's confusing comes up, I can usually help out. However, we are having a problem with the summing of power series, one area where I am sorely lacking.  After spending two hours on a question, we still cannot solve it and are always left with a $k$. Admittedly, I don't fully know what I am doing.     Evaluate $\displaystyle \sum_{k=1}^\infty\frac{x^k}{k(k+1)}$.   We do know that the answer is $1 + \dfrac{1-x}{x}\ln (1-x)$.  Any hints or help in the direction to go would be very much appreciated. $\|h(x)-h(y)\|\geq 3\|x-y\|$ prove that image of open is open Does mass distribution/center of mass affect free fall? An everyday is example would be cars. If you were to drop a car, not taking air resistance into account, would a front-heavy car tumble forward as it fell? And a car with a perfect 50/50 front/rear weight distribution fall straight? Does mass distribution/center of mass affect free fall? Or would they both fall straight down without tumbling? Can you explain why please? How to list files installed by a snap package? 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For example, I would say the idiom when I help someone remember something by giving it a shot in the dark and getting it right miraculously after some guesses.  What is the English idiom I'm looking for? How to integrate $\int_0^{\pi/2}\frac{\sin^nx}{\sin^nx+\cos^nx}dx$? Possible Duplicate:          How can we integrate $$\int_0^\frac{\pi}2\frac{\sin^nx}{\sin^nx+\cos^nx}\,\mathrm dx , \,\,\,\,\,\,\,\,\, n\in N \quad?$$ Thanks for any hint. What is the state-of-the-art method for automatically executing custom scripts upon USB device plug-in under current Linux distributions like Debian/CentOS/Fedora?  For example if you want to automatically mount/copy some files/umount a USB mass storage device based on its UUID (or device ID etc.). Recover accidentally removed files on NTFS partition I accidentally removed some files on a NTFS partition  How can I recover them staying inside Linux without rebooting ? Well, this is an exercise problem from Herstein which sounds difficult:   How does one prove that if $|G|&gt;2$, then $G$ has non-trivial automorphism?   The only thing I know which connects a group with its automorphism is the theorem, $$G/Z(G) \cong \mathcal{I}(G)$$ where $\mathcal{I}(G)$ denotes the Inner- Automorphism group of $G$. So for a group with $Z(G)=(e)$, we can conclude that it has a non-trivial automorphism, but what about groups with center? Word for two collections that do not have any elements in common I'm looking for a word for when you have a collection A and a collection B and they have no overlap.  In mathematical terms: the relation between two sets where the intersection is empty. Like in this Venn diagram:    The word that keeps popping up in my mind is disparate sets, but I don't feel that completely covers the meaning when I look at the definition, because that doesn't seem to preclude overlapping sets that are different:     disparate   1. distinct in kind; essentially different; dissimilar:   disparate ideas. If you cast Blindness/Deafness as a 3rd level spell, can you target one creature with both effects? SQL Servers has Traces and XEvents. These are used to capture and analyze what is going on with our SQL Server Instances. Events are stored in the stack for later analysis. For example,  If I decide to monitor any dead lock in the database, I just query the trace file to see the history of deadlock for a period of time. Here is my question:  While events occur, in our example deadlock event, is there a way to get an email notification using msdb.dbo.xp_send_dbmail? Why did the command ":(){ :|: & };:" make my system lag so badly I had to reboot? Do not run this command to 'test' it unless you are prepared for a crash and/or force-rebooting your system.  I was in my Virtualbox running 12.04 trying to compile an app, and while waiting I happened to chance upon a forum where a comment said:   Try :(){ :|: &amp; };:  Fun, too, and doesn't need root.  Without thinking, I ran it in my gnome-terminal. It made my 12.04(in Virtualbox) lag so badly, I had to shut it down. My question is what does this command do?   :(){ :|: &amp; };: