star trek - How was General Korok able to take control of a Borg Sphere, and in such a short amount of time?

Having rewatched the episodes, they don't provide a canonical answer. Here's what I've pieced together that's plausible.

Like the Queen said, she can no longer hear those drones. This is such an enormous threat that she is willing to self-destruct entire vessels. It's played as a ploy to influence Janeway, but the Queen also treats it like a deadly infection with no cure; the only solution is to destroy it and everything it has touched.

No matter how they accomplished it, the Borg Queen obviously views a single rogue drone as a threat.

QUEEN: Yes, a lot of damage. Spatial grid nine four, cube six three zero. Complement sixty four thousand drones. But I can no longer hear three of them. No doubt they've joined your resistance. Are they trying to sabotage the vessel and liberate others? I don't know, because I can no longer hear them. Initiate self-destruct.

Why are a few independent drones such a threat? In short, Borg internal security sucks.

The rogue Borg are still Borg. They still have Borg technology. They have the full knowledge of the Borg. But they're acing independently, no longer as part of The Collective. As Seven demonstrates repeatedly, The Borg have few defenses against their own kind. The idea of Borg fighting Borg is inconceivable. This is made far worse by their total trust of other Borg and complete sharing of all thoughts. If you are Borg, everything is wide open. This is demonstrated in Unimatrix Zero by...

• Every Borg ship has a Central Plexus which can be used to inject a virus into the entire fleet with relative ease. No firewall.


• The Borg Queen just assimilated the Voyager crew and puts them to work as drones. She fully trusts the assimilation process even with such cunning opponents.


• Tuvok and B'Elenna are able to walk through the Plexus's shielding simply because they are now Borg.


• B'Elenna, without even so much as a Tricorder, is able to bypass the Plexus's access codes fairly quickly indicating they're perfunctory.


• Nobody is guarding the Plexus.


• The Queen knows Tuvok is having independent thoughts, that he's a threat, yet she does not sound an alert. No extra defenses go up around the Plexus. She cannot seem to act until she gets information from a drone (Tuvok).


• Once Tuvok is assimilated, the Borg Queen goes right back to trusting him.

You mentioned in the comments a counter-point that...

Janeway, B'elanna, and Tuvok were all assimilated with Borg technology. They were on a Borg Vessel. They were independent. And the Borg had no problem taking them all captive in a short period of time. That was Borg attacking Borg.

I would answer that they were fully trusted up until the point the Queen realized they were disconnected from the Collective, it was a trick. It took a special intervention by the Queen to have them captured. You don't defeat the Borg by fighting them, you defeat the Borg by tricking them into trusting you. This is how the first Borg cube was destroyed in Best Of Both Worlds with the "sleep" order. Once that trust is lost, once you're no longer considered Borg, you're doomed.

This all makes sense given how the Borg consider all drones part of a single entity. Drones are assimilated enemies; using the Voyager crew as drones is situation normal. Only the Queen is able to make the conscious choice to kill a drone, analogous to cutting out cancerous cells.

I don't understand how a regular rogue Borg who is one in a million can influence or take over that many drones... How does that independent drone have power to override the entire collective?

As argued above, The Borg's weakness is their collective link. Trick the Borg into thinking you're Borg, and they have no defenses. Presumably rather than subduing tens of thousands of Borg, General Korok took command of the ship by taking control of the local consciousness, possibly a local equivalent to the Central Plexus, probably by knocking a few Borg heads together just to keep things Klingon. As I argued above, The Borg would have no defense against him.

How does that drone have more influence then the queen?

The Queen isn't psychic, she still relies on technology. Korok presumably subverted that technology with his local access to the hardware on the ship, analogous to hacking a computer by having physical access to it. If one plugs your computer into their corrupted network, they can do a lot of damage. It's been demonstrated before that Borg can lose their connection to the Collective. Pick any one, or make up a new one, Korok did that and then took over local command.

As to the ratio problem between the declared "one in a million" and the demonstrated one in ten thousand, I would suggest that means only one in a hundred Borg ships have a drone with the mutation.