Best approach for precise Rational arithmetics in MySQL
Is floating point math broken?
I am on Ubuntu and I have forgotten the password for my Gnome Keyring (yes, stupid me, I know). Any way I can get it back? I have already looked at , but it says it's not possible if my home directory is encrypted and unfortunately my home directory is encrypted. How to make sure that Qt5.4.2 is installed properly I installed qt5.4 from  in Ubuntu 14.04, but when I run:   qmake -v   I always get the old version Qt5.2.1, although I think it is installed here Qt version 5.4.2 in /opt/qt54/lib. Can anyone tell me how to make sure that Qt5.4.2 is installed properly?   Thanks question about the limit $\lim_{h\to0}\frac{\arcsin(x+h)-\arcsin(x)}{h}$ Poiseuille's law states that the rate of flow of water is proportionate to $r^4$ where $r$ is the radius of the pipe. I don't see why.  Intuitively I would expect rate of flow of fluid to vary with $r^2$ as the volume of a cylinder varies with $r^2$ for a constant length. The volume that flows past a point is equal to rate of flow fluid, and thus it should vary with $r^2$.  I cannot understand the mathematical proof completely. Is there an intuitive explanation for this? Prove that $\det(M-I)=0$ if $\det(M)=1$ and $MM^T=I$ $M$ is a $3 \times 3$ matrix such that $\det(M)=1$ and $MM^T=I$, where $I$ is the identity matrix. Prove that $\det(M-I)=0$  I tried to take $M$ $=$ $$ \begin{pmatrix}         a  &amp;b &amp; c \\         d &amp; e &amp; f \\         g &amp; h &amp; i         \end{pmatrix} $$   but its expansion is too long. Pass the output of previous command to next as an argument Is there a single word for "moving unhinderedly"? Cylindrical vs azimuthal symmetry What is the difference between cylindrical and azimuthal symmetry, are they the same? I have not been able to find a clear explanation of these terms wrt. a cylinder. I need to know which length I should integrate over to solve the problem below.  A cylinder of radius $R$ and length $L$ has a cylindrically symmetric volume charge density of $\rho(x)$. Calculate the total charge on the cylinder. Could you vs would you Could you write your name? Would you write your name?   When you are asked to do this, are there any situation in which you hear weird if either is used (but the other sounds pretty natural .) What is the command to open the shutdown dialog? I do not understand much about mine bitcoins, but I downloaded a program that is like a wallet, but I want to know how I do to mine. Has a calling GUIminder but is for windows, someone knows one that is for ubuntu? How do I set the default font size in Vim? Story about last 2 men on Earth. One very evil, and the other very ethical Why don't the Ubuntu repositories have the latest versions of software? How to prevent an email from accidentally being forwarded? Status of B1/B2 visa after citizenship change? I have a valid B1/B2 visa valid to US till March 2019 on Indian passport, I changed my citizenship to Australian. Is my B1/B2 visa on Indian passport valid? Show $\operatorname{Aut}(C_2 \times C_2)$ is isomorphic to $D_6$ (the group with $x^3=1$, $y^2=1$ and $xy=yx^2$).  I'm not really sure how to express the elements of $\operatorname{Aut}(C_2 \times C_2)$. Would it be sufficient to show the elements of $\operatorname{Aut}(C_2 \times C_2)$, find their order and show they bijectively map to every element of $D_6$ and satisfy $xy=yx^2$? Short science fiction film about a Midwest farmer who builds a bunker after finding a space plant Determining possible minimal polynomials for a rank one linear operator I have come across a question about determining possible minimal polynomials for a rank one linear operator and I am wondering if I am using the correct proof method.  I think that the facts needed to solve this problem come from the section on Nilpotent operators from Hoffman and Kunze's "Linear Algebra".     Question: Let $V$ be a vector space of dimension $n$ over the field $F$ and consider a linear operator $T$ on $V$ such that $\mathrm{rank}(T) = 1$.  List all possible minimal polynomials for $T$.   Sketch of Proof:   If $T$ is nilpotent then the minimal polynomial of $T$ is $x^k$ for some $k\leq n$.  So suppose $T$ is not nilpotent, then we can argue that $T$ is diagonalizable based on the fact that $T$ must have one nonzero eigenvalue otherwise it would be nilpotent (I am leaving details of the proof of diagonalization but it is the observation that the characteristic space of the nonzero eigenvalue is the range of T and has dimension $1$).  Thus the minimal polynomial of $T$ is just a linear term $x-c$.    Did I make a mistake assuming that $T$ can have only one nonzero eigenvalue?  Thanks for your help Not sure how to make tables, but:  For a binary operation $*$, and set $\{e,a,b,c\}$, in the Cayley table, $a*a$ can be filled with either the identity or an element different from both $e$ and $a$. If in the table the place for $a*a$ is filled with $e$, then the rest of the table can be filled out in two different ways.  What are the two different ways?  Thanks