combine png and tikz, scalingproblem
Image with axis
Proving that the triangle inequality holds for a metric on $\mathbb{C}$ Show that $(X,d)$ is a metric space where $X =\Bbb C $ and the distance function is defined as:   $$d(x,y) = \frac {2|x-y|}{\sqrt {1+|x|^2} +  \sqrt {1 + |y|^2}}, \text{ for } x,y \in \Bbb C.$$   I have done the proof of the first two propositions for being a metric, but I'm having a problem in proving the triangle inequality. What are the automorphisms acting on $Q\sqrt[3]{2}$ that fixes Q? Don't we have single sign-on for all Stack Exchange sites? I would like to use many sites in the Stack Exchange network, but I need to login to each site separately. Though it's easy, can't we solve this problem? I know each site has a different url :( but is there any way? Why is orbital angular momentum not 0 when spin and linear momentum are not collinear?   Why can it be 0 when spin and linear momentum are parallel?  Like in the example of a scalar field at rest decaying into an electron and a positron via interaction $\frac{1}{2}g\phi \bar{\Psi}\Psi $   If spin is along x axis and three-momenta is along z axis, decay rate will be 0 if two spins are opposite because orbital momentum is not 0 after decaying. When looking at a PDF document I often want to zoom-out to scroll quickly to its contents and get an overview.  However, when I zoom-out past a certain threshold (it seems to differ per PDF) Safari thinks I want to see the tab overview:    I have never found a use for this function, so it only causes annoyance.  Can I turn this tab overview off somehow? A solution that uncouples the pinch-to-zoom gesture from the functionality would also work.  I'm on Mountain Lion 10.8.5 with Safari 6.1.3. I'm looking for a symbol for skeptical consequence so that I can write that something, B, is a skeptical consequence of something else, A.  In a book I read it's written like \(A \vdash B\) or \(A \sststile{}{} B\) but the horizontal line is wavy like \sim, has the same width as the vertical line and does not vary in width. So, what I'm looking for is a binary relation symbol that is similar to the combination of the first two and the last relation in the following image:    That is, something similar to the following mockup but the wavy line should be such that it has a constant width and the same width as the vertical line:    I've tried  without success. Injecting variables into an import namespace Find the solution of following differential equation:     $$\frac{dy}{dx}=\frac{1}{xy(x^2 \sin (y^2)+1)}$$   Could someone hint me something to get through this problem? error while loading shared libraries: libssl.so.1.1 (and libcrypto.so.1.1) As you can see I'm missing libcrypto and libssl files. I locked out myself from my server after running apt-update and apt-upgrade, I'm running this from web console, because ssh nor any other program won't work because of missing SSL files.  I tried removing and installing apt install openssl so did libssl-dev and/or compiling own openssl from a distro. None of these create the needed .so files, I ran locate, those files are not present anywhere on the server. There's also libssl1.0.0 which cannot be reinstalled and removing it would cause removal of 700MB of packages that would literally kill server and delete all data. Java toString() using reflection? Show that if $\sqrt{a}+\sqrt{b}\neq 0$, then $\mathbb{Q}(\sqrt{a}+\sqrt{b}) = \mathbb{Q}(\sqrt{a},\sqrt{b}), \forall a,b\in\mathbb{Q}$ Area is calculating wrong using $area in field calculator (QGIS 2.8.1-Wien) Prove that if for every $x \in \mathbb{R}^N$ $Ax=Bx$ then $A=B$ I am stuck in a question for Algebraic Structures:  I need to prove: If given any ring $R$, for any $a$ in $R$ $a\cdot a=0$ then $a+a=0$.  (of course $+$, $*$ and $0$ regarding $R$)  I didn't find any question regarding this question. When to pronounce ‹s› as /z/ in the middle of words? How to change the snapping increment in different units? I would like to know how to change the increments used for snapping transforms.  This would be useful in a number of situations but my problem now is that when I change the units it does not scale the snapping increments to match.  So when holding down ctrl the cube snaps from here:    To here:    I would like it to snap to the 1 foot grid, or possibly any other amount I find useful.  It would also be nice to be able to change the rotation snap as well. What happens when I connect a 2 amp charger instead of the 0.7 amp charger provided? Possible Duplicate:             I have a phone with 0.7 amp charger. I also have a Galaxy Nexus with a 2 amp charger.  If I connect the 2 amp charger into my phone, will my phone blow up? Can a university revoke one's degree for his minor misconduct? Can't replace block with a Command Block I am making a Sell Shop, but I need to replace some things using /setblock.  For one of the replacements, I am using the command:  /setblock 579 62 1053 minecraft:command_block 0 replace {Command:"testfor @p {Inventory:[{id:"minecraft:log",Count:32b}]}",TrackOutput:0}  But it won't work! When I try it using a Command Block, I get this message:     [19:14:38]   Data tag parsing failed: Unexpected token 'm' at: minecraft:log",Count:32b}]}",TrackOutput:0   Is there any way I can fix this? Does an ability or spell grant me the bonus action with which to use it? The  description of casting times says that spells with a casting time of &quot;bonus action&quot; require a bonus action to cast (p. 79, emphasis mine):  Most spells require a single action to cast, but some spells require a bonus action, a reaction, or much more time to cast. Bonus Action A spell cast with a bonus action is especially swift. You must use a bonus action on your turn to cast the spell, provided that you haven't already taken a bonus action this turn. You can't cast another spell during the same turn, except for a cantrip with a casting time of 1 action.  It's pretty clear that bonus actions aren't automatic (p. 69):  You can take a bonus action only when a special ability, spell, or other feature of the game states that you can do something as a bonus action. You otherwise don't have a bonus action to take.  So to cast a spell like Healing Word (p. 93), do I  need to be granted a bonus action that I can use, or do I have a bonus action I can use?  I guess I'm unclear on whether I need to have a bonus action before I can spend it on something, or whether having an ability, spell, or whatnot that can be done as a bonus action grants me the bonus action I need to use it.