How to reduce database connection by making one PDO instance for your entire project
How to properly set up a PDO connection
modular arithmetic, solving $ax + b \equiv c \pmod d$? For example $151x - 294\equiv 44\pmod 7 $. How would I go about solving that?  The answer says to simplify it into the $ax\equiv b\pmod c $ form first, but I have no clue on how to get rid of the $294$... help? Add manually installed application to 'Show Applications' grid in Ubuntu 18.04 Do photons lose energy due to gravitational redshift? If so, where does the lost energy go? In the gravitational redshift, the frequency of photons radiated from some source is reduced. As the energy of a photon is given by $\hbar\omega$, if the frequency is reduced where is the lost energy? Declare IDisposable for the class or interface? Is abstract algebra (mostly?) restricted to $2$-ary operators? This may be due to my own pure ignorance but it's my experience that all abstract algebra I've been introduced to, both in actual courses and in self-studies only exclusively deals with algebraic objects consisting of a set together with one or more binary operators defined on that set, perhaps over some other algebraic structure. Not counting categories here, just "low-level"-ish stuff.  I'm an undergraduate so my knowledge is of course very limited but I can't help to wonder why I never stumble upon algebraic structures with $n$-ary operators? Is there a good reason for this, something along the lines of $n$-ary operators behave "badly" when $n&gt;2$ or is it just my ignorance because I'm a beginner in the field? When I'm in a phone call, I still get alerts for emails and texts. The noise will play and, if the phone is on Speaker, it will vibrate -- often leading the person I'm talking to wonder what that weird noise was.  Surely there must be a way to silence the phone while you're talking on it. It's very distracting to have beepings going off right next to your ear! List of Ubuntu Versions with Corresponding Linux Kernel Version Is there a list of Ubuntu versions with default corresponding Linux kernel versions somewhere?  I would specifically like to know the most recent version of Ubuntu that still used Linux Kernel 2.x. How did Newton discover his second law? I've always assumed/been told that Newton's 2nd law is an empirical law — it must be discovered by experiment. If this is the case, what experiments did Newton do to discover this? Is it related to his studies of the motion of the moon and earth? Was he able to analyze this data to see that the masses were inversely related to the acceleration, if we assume that the force the moon on the earth is equal to the force the earth exerts on the moon?   According to , the  reads:     Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.   Translated as:      Law II: The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd.   My question is how did Newton come to this conclusion? I get that he knew from  the idea of inertia, but this doesn't instantly tell us that the change in momentum must be proportional to the net force. Did Newton just assume this, or was there some experiment he performed to tell him this? Sylow Theorem Explanation The Sylow theorems say that all $p$-Sylow subgroups are conjugate.   Is that the only thing they are conjugate to? In other words could a $p$-Sylow subgroup also be conjugate to something that is not a $p$-Sylow group?   Or does the fact that every element with order dividing $p$ is in a $p$-Sylow group mean that that is never possible? Finding determinant of matrix without expanding show that determinant $$\left|\matrix{ x^2+L  &amp;  xy   &amp;   xz \\ xy   &amp;    y^2+L &amp;   yz \\ xz   &amp;    yz   &amp;   z^2+L \\ }\right| =  L^2(x^2+y^2+z^2+L)$$  without expanding by using the appropriate properties of determinant.  All i can do is LHS  $$x^2y^2z^2\left|\matrix{ 1+L/x^2  &amp; 1  &amp;   1 \\ 1   &amp;   1+L/y^2 &amp;   1 \\ 1  &amp;    1   &amp;   1+L/z^2 \\ }\right|$$ Probability that a k digit number does not contain certain digits What do the symbols on the main menu mean? If you swipe all the way to the left on the menu and then some, this sequence of symbols appears. (Do not pay any mind to the white circles: it's where I was holding my finger. The space between the first few and the last three symbols is also not present in game.)    What gives? How do I get the CPU temperature? How do I get the CPU temperature? Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $ Inspired by , I was wondering if there is a simple logical argument to   Show that $ a,b, \sqrt{a}+ \sqrt{b} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b} \in\mathbb Q $  Note that the original link is using a computational method, where as I am looking for a simple logical argument.  I tried (unjutifiably) to argue that if some of two square roots is rational then each one is rational, this is a different than the (incorrect) argument that if sum of two algebraic numbers is rational then each one is rational ( counter example $a=1-\sqrt{2},b= 1+\sqrt{2} $) If you have a statically allocated array, the Visual Studio debugger can easily display all of the array elements.  However, if you have an array allocated dynamically and pointed to by a pointer, it will only display the first element of the array when you click the + to expand it.  Is there an easy way to tell the debugger, show me this data as an array of type Foo and size X? How to prevent Round with hidden fractions Quantum entanglement as practical method of superluminal communication Better way of saying "those who are curious"? I am writing a note in which I want to ask (curious) readers to refer another paper. The phrase curious minded comes to mind, but it seems somewhat awkward.  Is there a better way to convey similar import? How do you find the modular inverse of $5\pmod{\!11}$ Calling future method from batch class?