Why openjdk-10 is missing in 18.04 PPA where openjdk-11 is available?
Why is OpenJDK 10 packaged as openjdk-11-*?
If a lens focuses all incoming light to a point, how do we get 2D images? How do lenses produce 2-dimensional images, if a lens bends all incoming rays of light to intersect at the focal point? Shouldn't this produce a single dot of light on a screen placed at the focal length?  This is basically the standard diagram that always shows up in textbooks:    I know this doesn't happen in real life--I used to use telescopes pretty frequently for work. The most in-focus image would be the one with the smallest diameters for the stars, which, of course, we think of point sources at infinity. But--the light from all stars (despite being at infinity) is not all focused at a single point. Instead, each star's light is focused at its own $(x,y)$ point on a 2D image.  I can't reconcile the theory as I understand it with any of my real-life experience with optics. What am I missing? Change all @username references in comments when a user changes their name? The fact that a user can change their name at will can lead to some confusion in the comments.  For instance, suppose a user named "foo" changes his name to "bar", all those comments signed by "foo" are now signed by "bar", but responses to "bar"'s comments still start with "@foo".  Could those "@foo" references in comments be changed to "@bar"?    A brief discussion on this has set me straight.  I didn't think it through.  Request withdrawn. The $n$ complex $n$th roots of a complex number $z$ Suppose $z$ is a nonzero complex number, so $z=re^{i\theta}$. Show that there are only $n$ distinct complex $n$-th roots, given by $r^{1/n}e^{i(2\pi k+\theta)/n}$ for $0\leq k\leq n-1$.   My proof: Let $z=re^{i\theta}\in\mathbb{C}$ and $a\in\mathbb{C}$ s.t. $a^{n}=z$. Let $a=\rho e^{i\varphi}$. Then, $a^{n}=(\rho e^{i\varphi})^{n}$. Setting $\rho^{n}e^{i\varphi n}=re^{i\theta}$ and rewriting in polar form, we get $$\rho^{n}(\cos(n\varphi)+i\sin(n\varphi))=r(\cos(θ)+i\sin(\theta)).$$ Thus $\rho^{n}=r$ $\rightarrow$ $\rho=r^{1/n}$ and $n\varphi=\theta\rightarrow\varphi=\theta/n$. Thus the roots of $a\in\mathbb{C}$ have the form $$r^{1/n}(\cos(\tfrac{\theta}{n})+i\sin(\tfrac{\theta}{n}))=r^{1/n}(\cos(\tfrac{\theta}{n}+2\pi j)+i\sin(\tfrac{\theta}{n}+2\pi j))$$ for some $j\in\mathbb{Z}$ due to the periodicity of trig functions. Then, $$r^{1/n}(\cos(\tfrac{\theta}{n}+2\pi j)+i\sin(\tfrac{\theta}{n}+2\pi j))=r^{1/n}e^{i\left(2\pi j+\tfrac{\theta}{n}\right)}=r^{1/n}e^{i(\theta+2\pi k)/n}$$ for $0\leq k\leq n-1 ,j=nk\in\mathbb{Z} $.  I feel like there could be a more concise way to put this. Ubuntu Server 20.04 Nvidia Driver Dependencies I had a hard time installing Nvidia drivers in a fresh install of Ubuntu 20.04.  Installing via sudo apt install nvidia-driver-430 resulted in a list of 542 packages to install.  I ended up spending a bit of manual effort to get the Nvidia-provided driver installed without nearly so many dependencies (only had to install gcc and make).  Is this massive number of dependencies normal for Ubuntu Server?  I did a very vanilla install without the GUI.  Reddit suggested I ask here, as their opinion is that I should just install from the default repos, but I felt that so many packages was absurd just to install a driver.  Edit for clarity: installing the nvidia-driver-430 package appears to install the entire Gnome shell, which I feel is unnecessary on a server. Dates and times: "on", "in", "at"? I’m often confused when I speak about times and dates. What is the rule for using on, in, and at in the following sentences?   I will do it ___ Tuesday. We married ___ March. He returned ___ the same day. Every day ___ the same time, I walk the dog. How to reduce VM size? How do I capture the milky way? Can the milky way actually be photographed ? I know the image is manipulated, and is probably a composite, but how do you capture such contrast in the milky way? Is an equitorially mounted scope required? Any advice or pointers are welcome, thanks.  I'm heading out towards much less light polluted areas middle of next week and I want to try some nighttime sky captures with my 7D.  Additional info: I just found  on wikipedia that says: 54s, tripod mounted 5D, 16mm lens, f/2.8, ISO800. What else do I need to be aware of? My 7D is only an APS-C and the widest lens I have is 19mm. I'm thinking that might not be wide enough to capture an interesting shot? Riemann and Darboux Integral of a product of two functions I have installed Ubuntu 12.04-64 bit on my Lenovo IdeaPad laptop, and the wired Ethernet (LAN) connection doesn't work.  Running the lspci -vv | grep Atheros command from the terminal shows me I have the AR8161 Gigabit Ethernet controller:  02:00.0 Ethernet controller: Atheros Communications Inc. AR8161 Gigabit Ethernet (rev 08)   This looks like a new product whose drivers are not built into Ubuntu.  How do I install drivers to get the AR8161 working? Random spawn location despite sleeping in a bed I am trying to make Minecraft harder, and one of the ways I wish to do this is to have a "pseudo-hardcore" mode where dying spawns you in a random location rather than completely locking you out of the world.  I intend to do this by setting the spawn radius to be very high.  However, I also want to make this "bed-proof" - that is, if someone places a bed and sleeps in it, I want the player to still be spawned in a random location, regardless of their personal spawn point.  How do I do this? Command blocks are fine, but data packs are not preferred. how many terms will there be once you collect terms with equal monomials? What is the sum of all the coefficients? Prove $(a^2+b^2)(c^2+d^2)\ge (ac+bd)^2$ for all $a,b,c,d\in\mathbb{R}$. Prove $(a^2+b^2)(c^2+d^2)\ge (ac+bd)^2$ for all $a,b,c,d\in\mathbb{R}$.  So $(a^2+b^2)(c^2+d^2) = a^2c^2+a^2d^2+b^2c^2+b^2d^2$  and $(ac+bd)^2 = a^2c^2+2acbd+b^2d^2$  So the problem is reduced to proving that $a^2d^2+b^2c^2\ge2acbd$ but I am not sure how to show that 35km commute possible? Currently, on every other day I commute to work which is a distance of 18km each way. I enjoy this ride but next year I may be moving to a place which will be about 35km from work. Questions:  1) Would it still be reasonable to commute this kind of distance each way once I have moved?  2) Google maps estimates that this distance would take 2 hours to complete. Would it be possible (depending on the bike and fitness) to do this distance in about an hour? How do I URL encode a string Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$ Suppose $f$ and $g$ are continuous on $[a,b]$ and that $f(a) &lt; g(a)$ but $f(b) &gt; g(b)$.   Prove that $f(x) = g(x)$ for some $x \in [a,b]$.     I did try and actually did get as far as coming up with $f-g$. Would I set $h(x)= f(x)- g(x)$ and say $h(a) &lt;x&lt; h(b)$? Using Vim I often want to replace a block of code with a block that I just yanked.  But when I delete the block of code that is to be replaced, that block itself goes into the register which erases the block I just yanked. So I've got in the habit of yanking, then inserting, then deleting what I didn't want, but with large blocks of code this gets messy trying to keep the inserted block and the block to delete separate.  So what is the slickest and quickest way to replace text in Vim?   is there a way to delete text without putting it into the register? is there a way to say e.g. "replace next word" or "replace up to next paragraph" or is the best way to somehow use the multi-register feature? Was Daenerys actually trying to hatch the eggs? I was reading @Aegon' s response   and I realized that I've never been clear on whether Dani was intentional in her pyre building to do blood magic and wake the dragons, or if she was just grieving Drogo and killing Mirri and her statement about "only death can pay for life" was a slap in the Maegi's face, since in the end she sacrificed her unborn child for the husk of Drogo.    I know she had tried baking the eggs previously and had felt like they could hatch then, but was clearly disappointed and chastised herself for foolishness when they did not. I don't recall inner monologue or statements after that where she said, "ya know what I should have done..."   I guess what I'm asking is whether there is evidence outside her statement to the Maegi that she was intentional in her blood magic rite or if the miracle was a happy accident? Can my friend and I play minecraft together with different mods? Difference between Sort and SortBy Can I use one of my attacks to cast a cantrip? In the D&amp;D campaign I am currently participating in, I am playing as a level 5 high elf champion (I actually just reached level 5 at the end of the last session).  As a High Elf, I got a free cantrip at first level, and chose the firebolt cantrip.  Here's what I'm wondering now: for the purposes of the extra attack feature, does firebolt (and similar cantrips) count as an attack?